1. The document discusses permutations and combinations, including the fundamental principle of multiplication, permutations with and without repetition, and conditional permutations.
2. It provides examples of determining the number of possible automobile classifications, maximum number of outfits without repeating clothes, and forming numbers using given digits with and without repetition.
3. Permutations are arrangements of objects, and the number of permutations is calculated using factorials, either as nPr or n!/(n-r)!. Combinations are similar but order does not matter.
This document presents a systematic approach for solving mixed intuitionistic fuzzy transportation problems. It begins with definitions of fuzzy sets, intuitionistic fuzzy sets, and triangular intuitionistic fuzzy numbers. It then formulates an intuitionistic fuzzy transportation problem and proposes a mixed intuitionistic fuzzy zero point method to find the optimal solution in terms of triangular intuitionistic fuzzy numbers. Finally, it provides the computational procedure and illustrates the method with a numerical example.
The document provides a sample paper for the Common Admission Test (CAT) with 20 multiple-choice questions covering quantitative ability, logical reasoning, and data interpretation. It also provides solutions and explanations for the questions. The sample paper is intended to help CAT exam preparation by providing practice questions.
This document contains a 50 question multiple choice test on quantitative aptitude topics including ratio and proportion, equations, simple and compound interest, permutations and combinations, sequences and series, limits and calculus, statistics, probability, sampling theory, and index numbers. The questions cover defining key terms, solving equations, evaluating integrals and limits, probability calculations, and data analysis concepts. The answer key is provided at the end.
Este documento describe el proyecto final de una base de datos creada en Access sobre una operadora de turismo. Se detalla la creación de tablas como Socios, Empleados y Clientes, así como la inclusión de campos de datos personales y fotografías. También se explica la generación de formularios para visualizar y modificar los registros de cada tabla, y la construcción de consultas para recuperar información de las diferentes tablas relacionadas. El objetivo final es aplicar los conocimientos adquiridos durante el semestre para crear una base de datos funcional de
The document defines permutations and combinations. A k-permutation is an ordered lineup of k objects taken from a set of n objects. The number of k-permutations of n objects is nPk = n!/(n-k)!. A k-combination is an unordered collection of k objects from a set of n objects. The number of k-combinations of n objects is nCk = n!/(n-k)!k!. Several examples are provided to illustrate calculating the number of permutations and combinations.
Aptitude Training - PERMUTATIONS AND COMBINATIONS 2Ajay Chimmani
I have taken coaching from NARESH INSTITUTE for CRT (Campus Recruitment Training). In these videos, I have explained all the questions with answer and how to approach for the question etc, in the same manner how they have taught to me at the time of training. Hope u like it.
Aptitude training playlist link :
https://www.youtube.com/playlist?list=PL3v9ipJOEEPfumKHa02HWjCfPvGQiPZiG
For full playlist of Interview puzzles videos :
https://www.youtube.com/playlist?list=PL3v9ipJOEEPfI4zt4ExamGJwndkvg0SFc
24 standard interview puzzles:
https://www.youtube.com/playlist?list=PL3v9ipJOEEPefIF4nscYOobim1iRBJTjw
for C and C++ questions, that are asked in the interviews, go through the posts in the link : http://comsciguide.blogspot.com/
for more videos, my youtube channel :
https://www.youtube.com/channel/UCvMy2V7gYW7VR2WgyvLj3-A
Asheesh Minhas is a SQA Executive with over 1 year of experience in software testing. He has experience in the full SDLC and STLC, including preparing test cases and documentation. He is proficient in bug tracking, load testing, database testing, and other technical skills. Currently he is testing several web and mobile applications at Trigma Solutions related to healthcare, government schemes, and other domains.
This document presents a systematic approach for solving mixed intuitionistic fuzzy transportation problems. It begins with definitions of fuzzy sets, intuitionistic fuzzy sets, and triangular intuitionistic fuzzy numbers. It then formulates an intuitionistic fuzzy transportation problem and proposes a mixed intuitionistic fuzzy zero point method to find the optimal solution in terms of triangular intuitionistic fuzzy numbers. Finally, it provides the computational procedure and illustrates the method with a numerical example.
The document provides a sample paper for the Common Admission Test (CAT) with 20 multiple-choice questions covering quantitative ability, logical reasoning, and data interpretation. It also provides solutions and explanations for the questions. The sample paper is intended to help CAT exam preparation by providing practice questions.
This document contains a 50 question multiple choice test on quantitative aptitude topics including ratio and proportion, equations, simple and compound interest, permutations and combinations, sequences and series, limits and calculus, statistics, probability, sampling theory, and index numbers. The questions cover defining key terms, solving equations, evaluating integrals and limits, probability calculations, and data analysis concepts. The answer key is provided at the end.
Este documento describe el proyecto final de una base de datos creada en Access sobre una operadora de turismo. Se detalla la creación de tablas como Socios, Empleados y Clientes, así como la inclusión de campos de datos personales y fotografías. También se explica la generación de formularios para visualizar y modificar los registros de cada tabla, y la construcción de consultas para recuperar información de las diferentes tablas relacionadas. El objetivo final es aplicar los conocimientos adquiridos durante el semestre para crear una base de datos funcional de
The document defines permutations and combinations. A k-permutation is an ordered lineup of k objects taken from a set of n objects. The number of k-permutations of n objects is nPk = n!/(n-k)!. A k-combination is an unordered collection of k objects from a set of n objects. The number of k-combinations of n objects is nCk = n!/(n-k)!k!. Several examples are provided to illustrate calculating the number of permutations and combinations.
Aptitude Training - PERMUTATIONS AND COMBINATIONS 2Ajay Chimmani
I have taken coaching from NARESH INSTITUTE for CRT (Campus Recruitment Training). In these videos, I have explained all the questions with answer and how to approach for the question etc, in the same manner how they have taught to me at the time of training. Hope u like it.
Aptitude training playlist link :
https://www.youtube.com/playlist?list=PL3v9ipJOEEPfumKHa02HWjCfPvGQiPZiG
For full playlist of Interview puzzles videos :
https://www.youtube.com/playlist?list=PL3v9ipJOEEPfI4zt4ExamGJwndkvg0SFc
24 standard interview puzzles:
https://www.youtube.com/playlist?list=PL3v9ipJOEEPefIF4nscYOobim1iRBJTjw
for C and C++ questions, that are asked in the interviews, go through the posts in the link : http://comsciguide.blogspot.com/
for more videos, my youtube channel :
https://www.youtube.com/channel/UCvMy2V7gYW7VR2WgyvLj3-A
Asheesh Minhas is a SQA Executive with over 1 year of experience in software testing. He has experience in the full SDLC and STLC, including preparing test cases and documentation. He is proficient in bug tracking, load testing, database testing, and other technical skills. Currently he is testing several web and mobile applications at Trigma Solutions related to healthcare, government schemes, and other domains.
Math 1300: Section 7- 4 Permutations and CombinationsJason Aubrey
The document discusses permutations and combinations. It provides definitions and examples of factorials, permutations of n objects taken r at a time, and combinations of n objects taken r at a time. It includes theorems on calculating the number of permutations and combinations. Examples are provided to demonstrate calculating permutations and combinations for different values of n and r.
This document contains 25 questions that appear to be from a placement exam for Amcat. The questions cover a range of topics including sorting algorithms, logarithms, arrays, linked lists, probability, and word problems. The full solutions to all the questions are available at the provided website URL.
This material is a part of PGPSE / CSE study material for the students of PGPSE / CSE students. PGPSE is a free online programme for all those who want to be social entrepreneurs / entrepreneurs
This document contains 13 examples of permutations and combinations problems from a Mathematics 4 class. It provides example problems involving passcode combinations, palindromes, paths on a grid, lottery number selection, triangles in an octagon, quiz answers, multiple choice exams, hamburger toppings, NBA championship series outcomes, poker hands, and donut flavors. The document is intended to illustrate different applications of permutations and combinations in mathematics.
The document introduces circular permutation as the number of ordered arrangements that can be made of n objects in a circle. It is calculated as (n-1)!. Several examples are provided to illustrate circular permutation for seating people around a table and arranging beads on a bracelet. The document also considers the number of ways 4 married couples can be seated if spouses sit opposite each other [(n-1)!/3!] or if men and women alternate [3! x 4! = 144].
Quantitative techniques basics of mathematics permutations and combinations_p...taniyakhurana
This document discusses quantitative techniques including permutations, combinations, and binomial coefficients. It provides formulas and examples for calculating permutations and combinations when arranging objects in different orders or selecting subsets of objects irrespective of order. It also discusses Pascal's triangle and using the divide-and-conquer technique to efficiently calculate binomial coefficients.
The document discusses permutations and combinations. It defines permutations as arrangements where order is important, and provides an example of finding the number of permutations of selecting 2 letters from a set of 3 letters. Combinations are arrangements where order is not important, and gives an example of finding the number of combinations of selecting 2 letters from a set of 3. It also presents the factorial formulas for permutations and combinations and provides examples of using them to calculate permutation and combination problems. Finally, it highlights the difference between permutations and combinations and provides 4 example problems to practice calculating permutations and combinations.
The document discusses permutations and combinations. It defines permutations as arrangements where order is important, and combinations as groupings where order is not important. It provides examples of calculating permutations and combinations using factorial notation and formulas. The differences between permutations and combinations are outlined. Conditions that can be applied, such as objects being together or separated, are also discussed along with how to handle them in calculations.
Here are the answers to the pre-assessment questions:
1. B
2. A
3. B
4. D
5. B
6. C
7. C
8. A
9. B
10. C
11. B
12. A
13. B
14. B
For the mini-research question, here is a suggested outline:
Conduct a mini-research or survey among your classmates to determine the following:
1. Number of students interested to join the FUN RUN activity
2. Possible date preference for the activity
3. Suggested registration fee and minimum pledges
4. Prizes for top 3 runners
This document discusses four common methods for collecting data in organizations: questionnaires, interviews, observation, and unobtrusive measures. Questionnaires can efficiently collect standardized responses but answers may not be fully honest. Interviews are more flexible and allow follow up questions but are resource intensive. Observation involves directly watching behaviors as they occur but can be subjective. Unobtrusive measures obtain existing records not requiring direct participation, helping diagnose performance objectively.
- The document discusses technical analysis, which uses patterns in stock prices and trading volume to predict future stock performance, rather than analyzing companies' financials.
- It outlines various technical analysis techniques like charting patterns, indicators like RSI and Bollinger Bands, and identifying support and resistance levels.
- Technical analysis is believed to be one of the oldest forms of security analysis and is still widely used today, though it also faces challenges from theories like the efficient market hypothesis.
This document discusses various methods of data collection in research. It describes 7 common methods: questionnaires, checklists, interviews, observation, records, experimental approaches, and survey approaches. For each method, it outlines the key aspects, such as how it is administered or structured, as well as advantages and disadvantages. It also discusses important considerations for developing research instruments and measuring variables in studies. The overall purpose is to provide guidance on selecting appropriate data collection techniques based on the research problem and design.
1) The document discusses equations including simple equations, simultaneous linear equations, quadratic equations, and cubic equations.
2) It provides examples of solving simple equations, simultaneous linear equations using elimination and cross multiplication, quadratic equations using the quadratic formula, and cubic equations by factoring.
3) The nature of roots of quadratic equations is examined, identifying whether roots are real/imaginary or equal/unequal based on the discriminant.
This document provides learning objectives and content about rational and irrational numbers for a Class 9 mathematics lesson. It begins by defining different types of numbers - natural, whole, integers, rational, and irrational - and provides examples. It then explains rational numbers as those that can be written as fractions p/q, and irrational numbers as those that cannot be expressed as fractions. Various methods are provided for representing and finding rational numbers between two given rational numbers, as well as representing irrational numbers on the number line. Finally, the document discusses operations involving rational and irrational numbers.
The document discusses standards for educational and professional testing. It provides information about the National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies. The document covers topics like quantitative ability, general mathematics review including arithmetic, exponents and roots, inequalities, fractions, decimals, and comparing fractions. It aims to refresh knowledge of basic mathematical concepts essential for testing.
The document discusses standards for educational and professional testing. It provides information about the National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies. It covers topics like quantitative ability, general mathematics review including arithmetic, exponents and roots, inequalities, fractions, decimals, and comparing fractions. The mathematics review section provides formulas, properties, and examples for key mathematical concepts to help candidates prepare.
CHAPTER 2 DBMS IN EASY WAY BY MILAN PATELShashi Patel
The document discusses the relational model for database management. It provides details on the structure of relational databases including domains, relations, and schemas. It describes fundamental relational algebra operations like selection, projection, join, and set operations. It also covers tuple and domain relational calculus as non-procedural query languages. The document provides examples of queries and operations on sample relations to illustrate relational concepts.
The document provides information on the TCS NQT exam structure and syllabus which includes sections on verbal ability, reasoning, numerical ability, programming logic, and hands-on coding questions in C/C++, Java, Perl, and Python. It also outlines the exam pattern for Capgemini which consists of online tests in pseudo code, English, behavioral questions, and games, followed by technical and HR interviews assessing programming concepts, operating systems, data structures, and DBMS. Sample coding problems and solutions are provided for finding the kth largest factor of a number and minimizing coin distribution to values between 1 to N.
Math 1300: Section 7- 4 Permutations and CombinationsJason Aubrey
The document discusses permutations and combinations. It provides definitions and examples of factorials, permutations of n objects taken r at a time, and combinations of n objects taken r at a time. It includes theorems on calculating the number of permutations and combinations. Examples are provided to demonstrate calculating permutations and combinations for different values of n and r.
This document contains 25 questions that appear to be from a placement exam for Amcat. The questions cover a range of topics including sorting algorithms, logarithms, arrays, linked lists, probability, and word problems. The full solutions to all the questions are available at the provided website URL.
This material is a part of PGPSE / CSE study material for the students of PGPSE / CSE students. PGPSE is a free online programme for all those who want to be social entrepreneurs / entrepreneurs
This document contains 13 examples of permutations and combinations problems from a Mathematics 4 class. It provides example problems involving passcode combinations, palindromes, paths on a grid, lottery number selection, triangles in an octagon, quiz answers, multiple choice exams, hamburger toppings, NBA championship series outcomes, poker hands, and donut flavors. The document is intended to illustrate different applications of permutations and combinations in mathematics.
The document introduces circular permutation as the number of ordered arrangements that can be made of n objects in a circle. It is calculated as (n-1)!. Several examples are provided to illustrate circular permutation for seating people around a table and arranging beads on a bracelet. The document also considers the number of ways 4 married couples can be seated if spouses sit opposite each other [(n-1)!/3!] or if men and women alternate [3! x 4! = 144].
Quantitative techniques basics of mathematics permutations and combinations_p...taniyakhurana
This document discusses quantitative techniques including permutations, combinations, and binomial coefficients. It provides formulas and examples for calculating permutations and combinations when arranging objects in different orders or selecting subsets of objects irrespective of order. It also discusses Pascal's triangle and using the divide-and-conquer technique to efficiently calculate binomial coefficients.
The document discusses permutations and combinations. It defines permutations as arrangements where order is important, and provides an example of finding the number of permutations of selecting 2 letters from a set of 3 letters. Combinations are arrangements where order is not important, and gives an example of finding the number of combinations of selecting 2 letters from a set of 3. It also presents the factorial formulas for permutations and combinations and provides examples of using them to calculate permutation and combination problems. Finally, it highlights the difference between permutations and combinations and provides 4 example problems to practice calculating permutations and combinations.
The document discusses permutations and combinations. It defines permutations as arrangements where order is important, and combinations as groupings where order is not important. It provides examples of calculating permutations and combinations using factorial notation and formulas. The differences between permutations and combinations are outlined. Conditions that can be applied, such as objects being together or separated, are also discussed along with how to handle them in calculations.
Here are the answers to the pre-assessment questions:
1. B
2. A
3. B
4. D
5. B
6. C
7. C
8. A
9. B
10. C
11. B
12. A
13. B
14. B
For the mini-research question, here is a suggested outline:
Conduct a mini-research or survey among your classmates to determine the following:
1. Number of students interested to join the FUN RUN activity
2. Possible date preference for the activity
3. Suggested registration fee and minimum pledges
4. Prizes for top 3 runners
This document discusses four common methods for collecting data in organizations: questionnaires, interviews, observation, and unobtrusive measures. Questionnaires can efficiently collect standardized responses but answers may not be fully honest. Interviews are more flexible and allow follow up questions but are resource intensive. Observation involves directly watching behaviors as they occur but can be subjective. Unobtrusive measures obtain existing records not requiring direct participation, helping diagnose performance objectively.
- The document discusses technical analysis, which uses patterns in stock prices and trading volume to predict future stock performance, rather than analyzing companies' financials.
- It outlines various technical analysis techniques like charting patterns, indicators like RSI and Bollinger Bands, and identifying support and resistance levels.
- Technical analysis is believed to be one of the oldest forms of security analysis and is still widely used today, though it also faces challenges from theories like the efficient market hypothesis.
This document discusses various methods of data collection in research. It describes 7 common methods: questionnaires, checklists, interviews, observation, records, experimental approaches, and survey approaches. For each method, it outlines the key aspects, such as how it is administered or structured, as well as advantages and disadvantages. It also discusses important considerations for developing research instruments and measuring variables in studies. The overall purpose is to provide guidance on selecting appropriate data collection techniques based on the research problem and design.
1) The document discusses equations including simple equations, simultaneous linear equations, quadratic equations, and cubic equations.
2) It provides examples of solving simple equations, simultaneous linear equations using elimination and cross multiplication, quadratic equations using the quadratic formula, and cubic equations by factoring.
3) The nature of roots of quadratic equations is examined, identifying whether roots are real/imaginary or equal/unequal based on the discriminant.
This document provides learning objectives and content about rational and irrational numbers for a Class 9 mathematics lesson. It begins by defining different types of numbers - natural, whole, integers, rational, and irrational - and provides examples. It then explains rational numbers as those that can be written as fractions p/q, and irrational numbers as those that cannot be expressed as fractions. Various methods are provided for representing and finding rational numbers between two given rational numbers, as well as representing irrational numbers on the number line. Finally, the document discusses operations involving rational and irrational numbers.
The document discusses standards for educational and professional testing. It provides information about the National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies. The document covers topics like quantitative ability, general mathematics review including arithmetic, exponents and roots, inequalities, fractions, decimals, and comparing fractions. It aims to refresh knowledge of basic mathematical concepts essential for testing.
The document discusses standards for educational and professional testing. It provides information about the National Testing Service Pakistan Overseas Scholarship Scheme for PhD Studies. It covers topics like quantitative ability, general mathematics review including arithmetic, exponents and roots, inequalities, fractions, decimals, and comparing fractions. The mathematics review section provides formulas, properties, and examples for key mathematical concepts to help candidates prepare.
CHAPTER 2 DBMS IN EASY WAY BY MILAN PATELShashi Patel
The document discusses the relational model for database management. It provides details on the structure of relational databases including domains, relations, and schemas. It describes fundamental relational algebra operations like selection, projection, join, and set operations. It also covers tuple and domain relational calculus as non-procedural query languages. The document provides examples of queries and operations on sample relations to illustrate relational concepts.
The document provides information on the TCS NQT exam structure and syllabus which includes sections on verbal ability, reasoning, numerical ability, programming logic, and hands-on coding questions in C/C++, Java, Perl, and Python. It also outlines the exam pattern for Capgemini which consists of online tests in pseudo code, English, behavioral questions, and games, followed by technical and HR interviews assessing programming concepts, operating systems, data structures, and DBMS. Sample coding problems and solutions are provided for finding the kth largest factor of a number and minimizing coin distribution to values between 1 to N.
This document discusses standards for educational and professional testing. It provides an overview of the content and format of quantitative ability questions that may appear on tests, including topics like arithmetic, algebra, geometry, and data analysis. It also reviews important mathematical concepts in each of these areas, such as properties of numbers, fractions, decimals, exponents, and inequalities. The document is intended to help candidates prepare for quantitative questions that adhere to established testing standards.
This document summarizes key concepts from Chapter 5 on counting principles, permutations, and combinations. It introduces the product rule and sum rule for counting the number of possible outcomes of multi-step processes. It then covers permutations, which are ordered arrangements, and combinations, which are unordered selections of elements from a set. Examples are provided to illustrate calculating permutations and combinations using formulas like P(n,r) and C(n,r). The chapter also discusses proof techniques like direct proof, proof by contradiction, and proof by contraposition.
This document provides an outline for teaching a stage 5 mathematics unit on surds and indices. It includes key ideas such as defining rational and irrational numbers, performing operations with surds, and using integers and fractions for index notation. Students will learn to distinguish between rational and irrational numbers, perform the four basic operations with surds, expand expressions involving surds, and convert between surd and index form. The unit aims to build students' understanding of the real number system.
The document discusses various topics related to numbers including:
1) Perfect numbers which are numbers whose factors sum to the number.
2) Classification of numbers as natural, whole, integers, rational, and irrational.
3) Rules for divisibility including by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15.
4) Formulas for finding cubes of two-digit numbers and number of zeros in expressions.
CLASS VII -operations on rational numbers(1).pptxRajkumarknms
This document discusses properties of operations on rational numbers. It covers:
1) Addition of rational numbers, including having the same or different denominators. Properties include closure, commutativity, and additive identity.
2) Subtraction of rational numbers and its properties, noting the difference property and lack of an identity element.
3) Multiplication of rational numbers by multiplying numerators and denominators. Properties are closure, commutativity, associativity, identity of 1, and annihilation by 0.
4) Distributive property relating multiplication and addition/subtraction of rational numbers.
The document discusses number systems and provides examples of different types of numbers. It begins by explaining how early humans counted items without a formal system of numbers. The key developments were the creation of numbers and the number zero, which allowed people to answer questions about quantities.
The document then reviews natural numbers, whole numbers, and integers. It introduces rational numbers as numbers that can be expressed as fractions. Rational numbers can be positive or negative. Any number that cannot be expressed as a rational number, such as the square root of 2, is considered irrational. Real numbers include all rational and irrational numbers.
Okay, let's think through this step-by-step:
* For 1 guest, you need 2 bags of spaghetti
* For 2 guests, you need 5 bags of spaghetti
* For 3 guests, you need 8 bags of spaghetti
Let's call the number of guests n. Then we can write:
For n = 1 guest, bags of spaghetti = 2
For n = 2 guests, bags of spaghetti = 5
For n = 3 guests, bags of spaghetti = 8
Looking at the pattern, it seems the number of bags increases by 3 each time the number of guests increases by 1.
So the rule is:
Number of bags of spaghetti
The document discusses standards for educational and professional testing in Pakistan. It provides information about the National Testing Service Pakistan (NTS), including their website and email contact. It also mentions that NTS administers an overseas scholarship scheme for PhD studies. The bulk of the document outlines content that will be covered on quantitative ability sections of tests, including arithmetic, algebra, geometry, and data analysis. It provides a detailed review of topics tested like arithmetic operations, exponents, roots, inequalities, and other mathematical concepts.
The document discusses standards for educational and professional testing in Pakistan. It provides information about the National Testing Service Pakistan (NTS), including their website and email contact information. It also mentions that NTS administers an overseas scholarship scheme for PhD studies. The bulk of the document discusses quantitative ability and provides a detailed review of general mathematics concepts relevant to quantitative reasoning tests, including arithmetic, exponents and roots, fractions, decimals, properties of zero and one, and inequalities.
This document discusses counting principles such as the product rule, sum rule, and subtraction rule. It also covers permutations and combinations. The product rule states that if a procedure can be broken into stages with m possible outcomes for the first stage and n for the second, the total number of ways to complete the procedure is m * n. Permutations refer to ordered arrangements and are calculated with n!/(n-r)!. Combinations refer to unordered arrangements and are calculated with n!/r!(n-r)!.
This document discusses multiplication of integers. It explains that there are three ways to write multiplication and covers multiplying positive and negative numbers. The key rules are:
- The product of two integers with the same sign is positive.
- The product of two integers with different signs is negative.
- Examples are provided to demonstrate multiplying integers, including using order of operations and evaluating expressions with integers.
Unit-1 Basic Concept of Algorithm.pptxssuser01e301
The document discusses various topics related to algorithms including algorithm design, real-life applications, analysis, and implementation. It specifically covers four algorithms - the taxi algorithm, rent-a-car algorithm, call-me algorithm, and bus algorithm - for getting from an airport to a house. It also provides examples of simple multiplication methods like the American, English, and Russian approaches as well as the divide and conquer method.
This presentation was provided by Racquel Jemison, Ph.D., Christina MacLaughlin, Ph.D., and Paulomi Majumder. Ph.D., all of the American Chemical Society, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...TechSoup
Whether you're new to SEO or looking to refine your existing strategies, this webinar will provide you with actionable insights and practical tips to elevate your nonprofit's online presence.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
Andreas Schleicher presents PISA 2022 Volume III - Creative Thinking - 18 Jun...EduSkills OECD
Andreas Schleicher, Director of Education and Skills at the OECD presents at the launch of PISA 2022 Volume III - Creative Minds, Creative Schools on 18 June 2024.
Gender and Mental Health - Counselling and Family Therapy Applications and In...PsychoTech Services
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
1. Permutations and
Combinations
Quantitative Aptitude & Business Statistics
2. The Fundamental Principle of
Multiplication
• If there are
• n1 ways of doing one operation,
• n2 ways of doing a second
operation, n3 ways of doing a
third operation , and so forth,
Quantitative Aptitude & Business
2
Statistics:Permutations and Combinations
3. • then the sequence of k
operations can be performed in
n1 n2 n3….. nk ways.
• N= n1 n2 n3….. nk
Quantitative Aptitude & Business
3
Statistics:Permutations and Combinations
4. Example 1
• A used car wholesaler has agents
who classify cars by size (full,
medium, and compact) and age (0
- 2 years, 2- 4 years, 4 - 6 years,
and over 6 years).
• Determine the number of possible
automobile classifications.
Quantitative Aptitude & Business
4
Statistics:Permutations and Combinations
5. Solution 0-2
2-4
Full(F) 4-6
>6
0-2
2-4
Medium 4-6
>6
(M)
0-2
2-4
Compact 4-6
(C) >6
The tree diagram enumerates all possible
classifications, the total number of which
is 3x4= 12. Quantitative Aptitude & Business
5
Statistics:Permutations and Combinations
6. Example 2
• Mr. X has 2 pairs of trousers, 3
shirts and 2 ties.
• He chooses a pair of trousers, a
shirt and a tie to wear everyday.
• Find the maximum number of
days he does not need to repeat
his clothing.
Quantitative Aptitude & Business
6
Statistics:Permutations and Combinations
7. Solution
• The maximum number of days
he does not need to repeat his
clothing is 2×3×2 = 12
Quantitative Aptitude & Business
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Statistics:Permutations and Combinations
8. 1.2 Factorials
• The product of the first n
consecutive integers is denoted
by n! and is read as “factorial n”.
• That is n! = 1×2×3×4×…. ×(n-1)
×n
• For example,
• 4!=1x2x3x4=24,
• 7!=1×2×3×4×5×6×7=5040.
• Note 0! defined to be 1.
Quantitative Aptitude & Business
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Statistics:Permutations and Combinations
9. •The product of any number of
consecutive integers can be
expressed as a quotient of two
factorials, for example,
• 6×7×8×9 = 9!/5! = 9! / (9 – 4)!
• 11×12×13×14×15= 15! / 10!
=15! / (15 – 5)!
In particular,
• n×(n – 1)×(n – 2)×...×(n – r + 1)
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Statistics:Permutations and Combinations
10. 1.3 Permutations
• (A) Permutations
• A permutation is an arrangement
of objects.
• abc and bca are two different
permutations.
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Statistics:Permutations and Combinations
11. • 1. Permutations with repetition
– The number of permutations of r
objects, taken from n unlike objects,
– can be found by considering the
number of ways of filling r blank
spaces in order with the n given
objects.
– If repetition is allowed, each blank
space can be filled by the objects in n
different ways.
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Statistics:Permutations and Combinations
12. 1 2 3 4 r
n n n n n
• Therefore, the number of
permutations of r objects,
taken from n unlike objects,
• each of which may be
repeated any number of times
= n × n × n ×.... × n(r factors) =
nr
Quantitative Aptitude & Business
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Statistics:Permutations and Combinations
13. 2. Permutations without repetition
• If repetition is not allowed,
the number of ways of filling
each blank space is one less
than the preceding one.
1 2 3 4 r
n n-1 n-2 n-3 n-r+1
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Statistics:Permutations and Combinations
14. Therefore, the number of
permutations of r objects, taken
from n unlike objects, each of
which can only be used once in
each permutation
=n(n— 1)(n—2) .... (n—r + 1)
Various notations are used to
represent the number of
permutations of a set of n
elements taken r at a time;
Quantitative Aptitude & Business
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Statistics:Permutations and Combinations
15. • some of them are n
P , Pr , P (n, r )
r n
n!
( n − r )!
Since
n( n − 1)(n − 2)....(n − r + 1)(n − r )...3 ⋅ 2 ⋅ 1
=
( n − r )...3 ⋅ 2 ⋅ 1
Prn , n Pr , P (n, r )
= n( n − 1)(n − 2)....(n − r + 1)
=P r
n
n!
We have P =
n
(n − r )!
r
Quantitative Aptitude & Business
15
Statistics:Permutations and Combinations
16. Example 3
• How many 4-digit numbers can be
made from the figures 1, 2, 3, 4, 5,
6, 7 when
• (a) repetitions are allowed;
• (b) repetition is not allowed?
Quantitative Aptitude & Business
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Statistics:Permutations and Combinations
17. • Solution
• (a) Number of 4-digit numbers
= 74 = 2401.
• (b) Number of 4 digit numbers
=7 ×6 ×5 ×4 = 840.
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Statistics:Permutations and Combinations
18. Example 4
• In how many ways can 10 men
be arranged
• (a) in a row,
• (b) in a circle?
• Solution
• (a) Number of ways is
= 3628800
10
P
10
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Statistics:Permutations and Combinations
19. • Suppose we arrange
the 4 letters A, B, C
and D in a circular A
arrangement as
shown.
D B
• Note that the
arrangements ABCD,
BCDA, CDAB and C
DABC are not
distinguishable.
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Statistics:Permutations and Combinations
20. • For each circular arrangement
there are 4 distinguishable
arrangements on a line.
• If there are P circular
arrangements, these yield 4P
arrangements on a line, which
we know is 4!.
4!
Hence P = = (4 − 1)!= 3!
4
Quantitative Aptitude & Business
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Statistics:Permutations and Combinations
21. Solution (b)
• The number of distinct circular
arrangements of n objects is
(n —1)!
• Hence 10 men can be arranged
in a circle in 9! = 362 880 ways.
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Statistics:Permutations and Combinations
22. (B) Conditional
Permutations
• When arranging elements in
order , certain restrictions may
apply.
• In such cases the restriction
should be dealt with first..
Quantitative Aptitude & Business
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Statistics:Permutations and Combinations
23. Example 5
How many even numerals between 200
and 400 can be formed by using 1, 2, 3, 4,
5 as digits
(a) if any digit may be repeated;
(b) if no digit may be repeated?
Quantitative Aptitude & Business
23
Statistics:Permutations and Combinations
24. • Solution (a)
• Number of ways of choosing the
hundreds’ digit = 2.
• Number of ways of choosing the
tens’ digit = 5.
• Number of ways of choosing the
unit digit = 2.
• Number of even numerals
between 200 and 400 is
2 × 5 × 2 = 20.
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Statistics:Permutations and Combinations
25. •Solution (b)
•If the hundreds’ digit is 2,
then the number of ways of choosing
an even unit digit = 1,
and the number of ways of choosing a
tens’ digit = 3.
•the number of numerals formed
1×1×3 = 3.
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Statistics:Permutations and Combinations
26. If the hundreds’ digit is 3, then the
number of ways of choosing an
even. unit digit = 2, and the
number of ways of choosing a tens’
digit = 3.
• number of numerals formed
= 1×2×3 = 6.
• the number of even numerals
between 200 and 400 = 3 + 6 =
9
Quantitative Aptitude & Business
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Statistics:Permutations and Combinations
27. Example 6
In how many ways can
7 different books be
arranged on a shelf
(a) if two particular
books are together;
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27
Statistics:Permutations and Combinations
28. • Solution (a)
• If two particular books are
together, they can be considered
as one book for arranging.
• The number of arrangement of 6
books
= 6! = 720.
• The two particular books can be
arranged in 2 ways among
themselves.
• The number of arrangement of 7
books with two particular books
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Statistics:Permutations and Combinations
29. (b) if two particular books are
separated?
• Solution (b)
• Total number of arrangement of 7
books = 7! = 5040.
• the number of arrangement of 7
books with 2 particular books
separated = 5040 -1440 = 3600.
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Statistics:Permutations and Combinations
30. (C) Permutation with
Indistinguishable Elements
• In some sets of elements there
may be certain members that
are indistinguishable from each
other.
• The example below illustrates
how to find the number of
permutations in this kind of
situation.
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30
Statistics:Permutations and Combinations
31. Example 7
In how many ways can the letters of
the word “ISOS CELES” be
arranged to form a new “word” ?
• Solution
• If each of the 9 letters of
“ISOSCELES” were different,
there would be P= 9! different
possible words.
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Statistics:Permutations and Combinations
32. • However, the 3 S’s are
indistinguishable from each
other and can be permuted in 3!
different ways.
• As a result, each of the 9!
arrangements of the letters of
“ISOSCELES” that would
otherwise spell a new word will
be repeated 3! times.
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Statistics:Permutations and Combinations
33. • To avoid counting repetitions
resulting from the 3 S’s, we must
divide 9! by 3!.
• Similarly, we must divide by 2! to
avoid counting repetitions
resulting from the 2
indistinguishable E’s.
• Hence the total number of words
that can be formed is
9! ÷3! ÷2! = 30240
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Statistics:Permutations and Combinations
34. • If a set of n elements has k1
indistinguishable elements of one
kind, k2 of another kind,
and so on for r kinds of elements,
then the number of permutations of
the set of n elements is
n!
k1!k 2 !⋅ ⋅ ⋅ ⋅ k r !
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Statistics:Permutations and Combinations
35. 1.4 Combinations
• When a selection of objects is
made with no regard being paid to
order, it is referred to as a
combination.
• Thus, ABC, ACB, BAG, BCA, CAB,
CBA are different permutation, but
they are the same combination of
letters.
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35
Statistics:Permutations and Combinations
36. • Suppose we wish to appoint a
committee of 3 from a class of 30
students.
• We know that P330 is the number of
different ordered sets of 3 students
each that may be selected from
among 30 students.
• However, the ordering of the
students on the committee has no
significance,
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36
Statistics:Permutations and Combinations
37. • so our problem is to determine
the number of three-element
unordered subsets that can be
constructed from a set of 30
elements.
• Any three-element set may be
ordered in 3! different ways, so
P330 is 3! times too large.
• Hence, if we divide P330 by 3!,the
result will be the number of
unordered subsets of 30
elements taken 3 at a time.
Quantitative Aptitude & Business
37
Statistics:Permutations and Combinations
38. • This number of unordered
subsets is also called the
number of combinations of 30
elements taken 3 at a time,
denoted by C330 and
1 30
C = P3
30
3
3!
30!
= = 4060
27!3!Quantitative Aptitude & Business
Statistics:Permutations and Combinations
38
39. • In general, each unordered r-
element subset of a given n-
element set (r≤ n) is called a
combination.
• The number of combinations of
n elements taken r at a time is
denoted by Cnr or nCr or C(n, r) .
Quantitative Aptitude & Business
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Statistics:Permutations and Combinations
40. • A general equation relating
combinations to permutations
is
1 n n!
C r = Pr =
n
r! (n − r )!r!
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40
Statistics:Permutations and Combinations
41. • Note:
• (1) Cnn = Cn0 = 1
• (2) Cn1 = n
• (3) Cnn = Cnn-r
Quantitative Aptitude & Business
41
Statistics:Permutations and Combinations
42. Example8
• If 167 C 90+167 C x =168 C x then x
is
• Solution: nCr-1+nCr=n+1 Cr
• Given 167 C90+167c x =168C x
• We may write
• 167C91-1 + 167 C91=167+1 C61
• =168 C91
• X=91
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Statistics:Permutations and Combinations
43. Example9
• If 20 C 3r= 20C 2r+5 ,find r
• Using nCr=nC n-r in the right –side
of the given equation ,we find ,
• 20 C 3r =20 C 20-(2r+5)
• 3r=15-2r
• r=3
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43
Statistics:Permutations and Combinations
44. Example 10
• If 100 C 98 =999 C 97 +x C 901 find x.
• Solution 100C 98 =999C 98 +999C97
• = 999C901+999C97
• X=999
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44
Statistics:Permutations and Combinations
45. Example11
• If 13 C 6 + 2 13 C5 +13 C 4 =15 C x ,the value of
x is
• Solution :
• 15C x= 13C 6 + 13 C 5 + 13 C 4 =
• =(13c 6+13 C 5 ) +
• (13 C 5 + 13 C 4)
• = 14 C 6 +14 C 5 =15C6
• X=6 or x+6 =15
• X=6 or 8
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45
Statistics:Permutations and Combinations
46. Example12
• If n C r-1=36 ,n Cr =84 and n C r+1 =126 then
find r
• Solution
nCr 84 7
= =
nCr −1 36 3
• n-r+1 =7/3 * r
• 3/2 (r+1)+1 =7/3 * r
• nCr +1 126 3 r=3
= =
nCr 84 2
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46
Statistics:Permutations and Combinations
47. Example 13
• How many different 5-card
hands can be dealt from a deck
of 52 playing cards?
Quantitative Aptitude & Business
47
Statistics:Permutations and Combinations
48. Solution
• Since we are not concerned with
the order in which each card is
dealt, our problem concerns the
number of combinations of 52
elements taken 5 at a time.
• The number of different hands is
C525= 2118760.
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48
Statistics:Permutations and Combinations
49. Example 14
6 points are given and no three of
them are collinear.
(a) How many triangles can be
formed by using 3 of the given
points as vertices?
Quantitative Aptitude & Business
49
Statistics:Permutations and Combinations
50. Solution:
• Solution
• (a) Number of triangles
• = number of ways
• of selecting 3 points out of 6
• = C63 = 20.
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Statistics:Permutations and Combinations
51. • b) How many pairs of triangles
can be formed by using the 6
points as vertices ?
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51
Statistics:Permutations and Combinations
52. • Let the points be A, B, C, D, E, F.
• If A, B, C are selected to form a
triangles, then D, E, F must form
the other triangle.
• Similarly, if D, E, F are selected to
form a triangle, then A, B, C must
form the other triangle.
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52
Statistics:Permutations and Combinations
53. • Therefore, the selections A, B,
C and D, E, F give the same pair
of triangles and the same
applies to the other selections.
• Thus the number of ways of
forming a pair of triangles
= C63 ÷ 2 = 10
Quantitative Aptitude & Business
53
Statistics:Permutations and Combinations
54. Example 15
• From among 25 boys who play
basketball, in how many different
ways can a team of 5 players be
selected if one of the players is to
be designated as captain?
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54
Statistics:Permutations and Combinations
55. Solution
• A captain may be chosen from any of the 25
players.
• The remaining 4 players can be chosen in C254
different ways.
• By the fundamental counting principle, the
total number of different teams that can be
formed is
25 × C244=265650.
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55
Statistics:Permutations and Combinations
56. (B) Conditional
Combinations
• If a selection is to be
restricted in some way, this
restriction must be dealt with
first.
• The following examples
illustrate such conditional
combination problems.
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56
Statistics:Permutations and Combinations
57. A committee of 3 men
and 4 women is to be
selected from 6 men and
9 women.
If there is a married
couple among the 15
persons, in how many
ways can the committee
be selected so that it
contains the married
Quantitative Aptitude & Business
57
Statistics:Permutations and Combinations
58. • Solution
• If the committee contains the
married couple, then only 2 men
and 3 women are to be selected
from the remaining 5 men and 8
women.
• The number of ways of selecting 2
men out of 5 = C52 = 10.
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Statistics:Permutations and Combinations
59. • The number of ways of selecting
3 women out of 8 =C83 = 56.
• the number of ways of selecting
the committee = lO × 56 = 560.
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Statistics:Permutations and Combinations
60. Example 17
• Find the number of ways a team
of 4 can be chosen from 15 boys
and 10 girls if
(a) it must contain 2 boys and 2
girls,
Quantitative Aptitude & Business
60
Statistics:Permutations and Combinations
61. • Solution (a)
• Boys can be chosen in C152 = 105
ways
• Girls can be chosen in C102 = 45
ways.
• Total number of ways is 105 × 45
= 4725.
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61
Statistics:Permutations and Combinations
62. (b) it must contain at least 1 boy and 1
girl.
• Solution :
• If the team must contain at least 1
boy and 1 girl it can be formed in
the following ways:
• (I) 1 boy and 3 girls, with C151 × C103
= 1800 ways,
• (ii) 2 boys and 2 girls, with 4725
ways,
• (iii) 3 boys and 1 girl, with C153 ×
C101 = 4550 ways.
Quantitative Aptitude & Business
• the total number of teams is
62
Statistics:Permutations and Combinations
63. Example 18
• Mr. .X has 12 friends and
wishes to invite 6 of them to a
party. Find the number
of ways he may do this if
(a) there is no restriction on
choice,
Quantitative Aptitude & Business
63
Statistics:Permutations and Combinations
64. • Solution (a)
• An unrestricted choice of 6
out of 12 gives C126= 924.
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Statistics:Permutations and Combinations
65. two of the friends is a couple
• (b)
and will not attend separately,
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65
Statistics:Permutations and Combinations
66. B Solution
• If the couple attend, the
remaining 4 may then be chosen
from the other 10 in C104 ways.
• If the couple does not attend,
then He simply chooses 6 from
the other 10 in C106 ways.
• total number of ways is C104 +
C106 = 420.
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Statistics:Permutations and Combinations
67. Example 19
Find the number of ways in which
30 students can be divided into
three groups, each of 10 students,
if the order of the groups and the
arrangement of the students in a
group are immaterial.
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67
Statistics:Permutations and Combinations
68. • Solution
• Let the groups be denoted by A,
B and C. Since the arrangement
of the students in a group is
immaterial,
• group A can be selected from
the 30 students in C3010 ways .
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Statistics:Permutations and Combinations
69. • Group B can be selected from the
remaining 20 students in C2010
ways.
• There is only 1 way of forming
group C from the remaining 10
students.
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Statistics:Permutations and Combinations
70. • Since the order of the groups is
immaterial, we have to divide
the product C3010 × C2010 × C1010
by 3!,
• hence the total number of ways
of forming the three groups is
1
× C3 × C10 × C10
30 20 10
3!
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70
Statistics:Permutations and Combinations
71. Example20
• If n Pr = 604800 10 C r =120 ,find
the value of r
• We Know that nC r .r P r = nPr .
• We will use this equality to find r
• 10Pr =10Cr .r|
• r |=604800/120=5040=7 |
• r=7
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Statistics:Permutations and Combinations
72. Example 21
• Find the value of n and r
• n Pr = n P r+1 and
n C r = n C r-1
Solution : Given n Pr = n P r+1
n –r=1 (i)
n C r = n C r-1 n-r = r-1 (ii)
Solving i and ii
r=2 and n=3
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Statistics:Permutations and Combinations
73. Multiple choice Questions
Quantitative Aptitude & Business
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Statistics:Permutations and Combinations
74. 1. Eleven students are
participating in a race. In how
many ways the first 5 prizes can
be won?
A) 44550
B) 55440
C) 120
D) 90
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Statistics:Permutations and Combinations
75. 1. Eleven students are
participating in a race. In how
many ways the first 5 prizes can
be won?
A) 44550
B) 55440
C) 120
D) 90
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Statistics:Permutations and Combinations
76. • 2. There are 10 trains plying between
Calcutta and Delhi. The number of ways in
which a person can go from Calcutta to Delhi
and return
• A) 99.
• B) 90
• C) 80
• D) None of these
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Statistics:Permutations and Combinations
77. • 2. There are 10 trains plying between
Calcutta and Delhi. The number of ways in
which a person can go from Calcutta to Delhi
and return
• A) 99.
• B) 90
• C) 80
• D) None of these
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Statistics:Permutations and Combinations
78. • 3. 4P4 is equal to
• A) 1
• B) 24
• C) 0
• D) None of these
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Statistics:Permutations and Combinations
79. • 3. 4P4 is equal to
• A) 1
• B) 24
• C) 0
• D) None of these
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79
Statistics:Permutations and Combinations
80. • 4.In how many ways can 8
persons be seated at a round
table?
• A) 5040
• B) 4050
• C) 450
• D) 540
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80
Statistics:Permutations and Combinations
81. • 4.In how many ways can 8
persons be seated at a round
table?
• A) 5040
• B) 4050
• C) 450
• D) 540
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Statistics:Permutations and Combinations
82. n n+1
• 5. If
P13 : P12 =3 : then
4
value of n is
• A) 15
• B) 14
• C) 13
• D) 12
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Statistics:Permutations and Combinations
83. n n+1
• 5. If
P13 : P12 =3 : then
4
value of n is
• A) 15
• B) 14
• C) 13
• D) 12
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Statistics:Permutations and Combinations
84. • 6.Find r if 5Pr = 60
• A) 4
• B) 3
• C) 6
• D) 7
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84
Statistics:Permutations and Combinations
85. • 6.Find r if 5Pr = 60
• A) 4
• B) 3
• C) 6
• D) 7
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85
Statistics:Permutations and Combinations
86. • 7. In how many different ways can
seven persons stand in a line for a
group photograph?
• A) 5040
• B) 720
• C) 120
• D) 27
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86
Statistics:Permutations and Combinations
87. • 7. In how many different ways can
seven persons stand in a line for a
group photograph?
• A) 5040
• B) 720
• C) 120
• D) 27
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87
Statistics:Permutations and Combinations
88. • 8. If 18 Cn = 18 Cn+ 2 then the value
of n is ______
A) 0
B) –2
C) 8
D) None of above
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88
Statistics:Permutations and Combinations
89. • 8. If 18 Cn = 18 Cn+ 2 then the value
of n is ______
A) 0
B) –2
C) 8
D) None of above
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Statistics:Permutations and Combinations
90. • 9. The ways of selecting 4 letters
from the word EXAMINATION is
• A) 136.
• B) 130
• C) 125
• D) None of these
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90
Statistics:Permutations and Combinations
91. • 9. The ways of selecting 4 letters
from the word EXAMINATION is
• A) 136.
• B) 130
• C) 125
• D) None of these
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91
Statistics:Permutations and Combinations
92. • 10 If 5Pr = 120, then the value of
r is
• A) 4,5
• B) 2
• C) 4
• D) None of these
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Statistics:Permutations and Combinations
93. • 10 If 5Pr = 120, then the value of
r is
• A) 4,5
• B) 2
• C) 4
• D) None of these
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Statistics:Permutations and Combinations