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The document discusses circular permutations, which refer to arrangements of objects in a circular manner without distinction between clockwise and counterclockwise order. It provides examples of calculating the number of possible circular permutations for different numbers of objects. Specifically, it explains that the number of permutations is (n-1)!/2 when clockwise and counterclockwise orders are indistinguishable, and (n-1)! when they are distinguishable, where n is the number of objects. The document also provides examples of applying these formulas to problems involving arranging people or objects in a circular configuration.

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Math 8 - Linear Inequalities in Two Variables

This document is a math lesson plan on linear inequalities in two variables taught by Mr. Carlo Justino J. Luna at Malabanias Integrated School in Angeles City. The lesson introduces linear inequalities and their notation, defines them as having two linear expressions separated by symbols like greater than and less than, and shows examples of inequalities in two variables. It then discusses how to determine if an ordered pair is a solution by substituting into the inequality. Finally, it explains how to graph linear inequalities in two variables by first rewriting them as equations and then plotting intercepts and shading the appropriate region based on a test point.

Combined variation

The document describes a problem involving combined variation, where the variable z varies jointly as w and x, and inversely as y. It gives the equation of variation as z = kwx/y, where k is the constant of variation. It solves for k when z = 100, w = 4, x = 5, and y = 15, finding that k = 75. Therefore, the equation of combined variation is z = 75wx/y. It then uses this to solve for z when w = 1, x = 5, and y = 3, finding that z = 125.

A detailed lesson plan in permutation

The document is a detailed lesson plan for a mathematics class on permutation. It outlines the objectives, content, materials, and procedures for the lesson. The lesson will teach students about permutation rules including n!, nPr, and arrangements of distinct objects. Example problems are provided to demonstrate each rule, and students will complete activities in groups to practice the rules and verify their understanding.

Rational Expressions

To solve this rational equation, we first find the LCD of the fractions, which is x^2(x-5)(x-6). Then we multiply both sides of the equation by the LCD:
x^2(x-5)(x-6) = x^2(x-5)(x-6)
Canceling the common factors, we obtain:
x^2 = x^2
Since this holds for all real values of x, the solution is all real numbers. Therefore, the solution is x ∈ R.

Solving Equations Transformable to Quadratic Equation Including Rational Alge...

Provides examples and solutions on how to solve equations that is transformable to quadratic equation and rational algebraic equations.

Integral Exponents

This document discusses integral exponents and how to evaluate expressions with zero and negative exponents. It provides examples of simplifying expressions with zero and negative exponents by using the definition that a negative exponent means to take the reciprocal of the base and raise it to the positive value of the exponent. It also explains that any nonzero number raised to the zero power is equal to 1, and expressions should be rewritten with only positive exponents.

Grade 8-if-then-statement

Here are the converses, inverses, and contrapositives of the given statements:
1. Conditional: If two angles form a linear pair, then they are supplementary.
Converse: If two angles are supplementary, then they form a linear pair.
Inverse: If two angles do not form a linear pair, then they are not supplementary.
Contrapositive: If two angles are not supplementary, then they do not form a linear pair.
2. Conditional: If a parallelogram has a right angle, then it is a rectangle.
Converse: If a parallelogram is a rectangle, then it has a right angle.
Inverse: If a parallelogram does not have

joint variation

z = kxy
z = -12
z = kxy
z = -84
z = kxy
z = -21
4.
a. Combined means together as a whole.
b. Combined variation is when a quantity varies jointly with respect to the product of two or more variables.
c. The mathematical statement that represents combined variation is a = k(bc) where a varies jointly as b and c multiplied together.

Graphing polynomial functions (Grade 10)

This document provides instructions on graphing polynomial functions. It discusses identifying the roots, x-intercepts, and y-intercept from the factored form of the polynomial. It shows working through an example of graphing the function y = (x – 2)(x – 1)(x + 3). The key steps are:
1. Identify the roots and y-intercept
2. Arrange the roots in a table
3. Complete the table by calculating y-values for different x-values
4. Plot the points on a graph
5. Sketch the graph

Angles formed by parallel lines cut by transversal

If parallel lines are cut by a transversal, eight angles are formed that have specific relationships. Corresponding angles are congruent. Alternate interior angles and alternate exterior angles are congruent. Interior angles and exterior angles on the same side of the transversal are supplementary. The document provides examples of angle measurements that illustrate these properties and includes practice problems asking to determine angle measures using these relationships.

Simplifying Rational Algebraic Expressions

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Math 8 – congruent triangles

This document discusses congruent triangles and the corresponding parts theorem. It defines the three postulates used to prove congruence: SSS, SAS, and ASA. It provides an example of using the SSS postulate and corresponding parts theorem to show that two angles are congruent and find the exact measure of one of the angles. It emphasizes that corresponding parts theorem can only be used after triangles are shown to be congruent.

Cartesian Coordinate Plane - Mathematics 8

This document explains the Cartesian coordinate plane. It describes how the plane is divided into four quadrants by the x and y axes which intersect at the origin. It provides examples of plotting points using ordered pairs with coordinates (x,y). The document also notes that Rene Descartes developed this system by combining algebra and geometry. It includes an activity for students to physically position themselves on the x and y axes to learn the coordinate system.

Grade 9 Mathematics Module 6 Similarity

This document provides information about a mathematics module on similarity for grade 9 learners. It was collaboratively developed by educators from various educational institutions in the Philippines. The module aims to teach learners about proportions, similarity of polygons, conditions for similarity of triangles using various theorems, applying similarity to solve real-world problems involving proportions and similarity. It includes a module map, pre-assessment questions to gauge learners' prior knowledge, and covers topics like proportions, similarity of polygons and triangles, and applying similarity concepts to solve problems.

2.7.4 Conditions for Parallelograms

* Prove that a given quadrilateral is a parallelogram.
* Prove that a given quadrilateral is a rectangle, rhombus, or square.

COT2 Lesson Plan Grade 8

This document is a daily lesson log for an 8th grade mathematics class. It outlines the objectives, content, learning procedures, and evaluation for a lesson on linear equations in two variables. The objectives are for students to identify and solve linear equations with two variables and present solutions accurately. The content covers the standard form of these equations and how to find ordered pairs and graph the linear equations. The learning procedures take students through a review, examples of linear equations with two variables, how to solve and graph them, practice problems, and an evaluation.

Mathematics 9 Variations

This learner's module discusses about the topic Variations. It also discusses the definition of Variation. It also discusses or explains the types of Variations. It also shows the examples of the Types of Variations.

Linear Equations in Two Variables

The document discusses linear equations in two variables. It defines a linear equation as one that can be written in the standard form Ax + By = C, where A, B, and C are real numbers and A and B cannot both be zero. Examples are provided of determining if equations are linear and identifying the A, B, and C components if they are linear. The document also discusses using ordered pairs as solutions to linear equations and finding multiple solutions to a given linear equation.

Rectangular coordinate system

This document defines and explains the rectangular coordinate system. It begins by introducing Rene Descartes as the "Father of Modern Mathematics" who developed the Cartesian plane. The Cartesian plane is composed of two perpendicular number lines that intersect at the origin (0,0) and divide the plane into four quadrants. Each point on the plane is identified by an ordered pair (x,y) denoting its distance from the x-axis and y-axis. The sign of the x and y values determines which quadrant a point falls into. Examples are provided to identify points and their corresponding quadrants.

Direct variation power point

The document defines direct variation and provides examples of how to determine if a relationship is direct variation. It explains that direct variation can be represented by an equation in the form of y=kx, where k is the constant of variation. It gives examples of determining the constant of variation from tables of x and y values and using the constant to find unknown values. It also provides examples of solving word problems using direct variation.

Math 8 - Linear Inequalities in Two Variables

Math 8 - Linear Inequalities in Two Variables

Combined variation

Combined variation

A detailed lesson plan in permutation

A detailed lesson plan in permutation

Rational Expressions

Rational Expressions

Solving Equations Transformable to Quadratic Equation Including Rational Alge...

Solving Equations Transformable to Quadratic Equation Including Rational Alge...

Integral Exponents

Integral Exponents

Grade 8-if-then-statement

Grade 8-if-then-statement

joint variation

joint variation

Graphing polynomial functions (Grade 10)

Graphing polynomial functions (Grade 10)

Angles formed by parallel lines cut by transversal

Angles formed by parallel lines cut by transversal

Simplifying Rational Algebraic Expressions

Simplifying Rational Algebraic Expressions

Math 8 – congruent triangles

Math 8 – congruent triangles

Cartesian Coordinate Plane - Mathematics 8

Cartesian Coordinate Plane - Mathematics 8

Grade 9 Mathematics Module 6 Similarity

Grade 9 Mathematics Module 6 Similarity

2.7.4 Conditions for Parallelograms

2.7.4 Conditions for Parallelograms

COT2 Lesson Plan Grade 8

COT2 Lesson Plan Grade 8

Mathematics 9 Variations

Mathematics 9 Variations

Linear Equations in Two Variables

Linear Equations in Two Variables

Rectangular coordinate system

Rectangular coordinate system

Direct variation power point

Direct variation power point

MATHEMATICS 10_4TH QUARTER_PERMUTATION.pptx

1. The document discusses permutation, which is the arrangement of objects in a definite order without repetition. It provides examples of calculating permutations using factorials for arrangements of objects, letters in words, and seating arrangements.
2. The fundamental counting principle and different types of permutations are explained, including permutation of n objects, distinguishable permutation, permutation of n objects taken r at a time, and circular permutation.
3. Examples are provided to demonstrate calculating permutations for a variety of scenarios involving arrangements of objects, letters, people, and keys to illustrate the different permutation concepts.

CYCLIC PERMUTATION.pptx

This document discusses cyclic permutation and provides examples of solving cyclic permutation problems. It defines cyclic permutation as arranging distinct objects around a fixed circle. The number of permutations when arranging n distinct objects in a circle is (n-1)!. It also provides the formula for arranging objects on a key ring or bracelet as (n-1)!/2. The document gives several examples of solving cyclic permutation problems and directs the reader to solve additional problems showing their work.

CIRCULAR PERMUTATION_grade 10_solves problems involving permutations

This document discusses circular permutations and how to calculate the number of possible arrangements of objects arranged in a circular manner. It begins by defining a circular permutation as the arrangement of objects around in a circular fashion. It then provides the formula to calculate the number of circular permutations of n different objects as P=(n-1)!. Several examples are given to demonstrate how to use the formula to solve problems involving arranging people, keys, beads or other objects in a circular configuration.

CIRCULAR PERMUTATION QUESTIONS AND LOGIC

CIRCULAR PERMUTATION QUESTIONS

Pre-Cal 40S May 6, 2009

This document discusses permutations of non-distinguishable objects and circular permutations. It provides examples of counting permutations of letters in words and arrangements of people or objects in a circle. Formulas are given for counting permutations of non-distinguishable objects as well as circular permutations, with the special case of circular bracelets which can be flipped over.

Pre-Cal 40S Slides November 28, 2007

This document discusses circular permutations and how to calculate the number of arrangements of objects around a circular table or circular bracelet. It provides the formula (n-1)! to calculate the number of arrangements of n objects in a circle. It also notes that for a circular bracelet that can be flipped over, the number of arrangements is (n-1)!/2. Examples are given for calculating the number of arrangements of people seated at a circular table and beads on a circular bracelet.

8 klas anglijska_mova_kuchma_2016

Here are the verbs in the be going to form:
1. What you (are going to) do with this room? — I (am going to) paint the walls in black and white.
2. The men in the helicopter (are going to) try to help the man in the water.
3. These two men (are going to) cycle across Africa.
4. The man is standing up. He (is going to) make a speech.
5. He (is going to) grow a beard when he leaves school.
6. You (are going to) reserve a seat?
7. I (am going to) plant an apple tree here.
8. I (

8 am kuch_2016

Here are the verbs in the be going to form:
1. What you (are going to) do with this room? — I (am going to) paint the walls in black and white.
2. The men in the helicopter (are going to) try to help the man in the water.
3. These two men (are going to) cycle across Africa.
4. The man is standing up. He (is going to) make a speech.
5. He (is going to) grow a beard when he leaves school.
6. You (are going to) reserve a seat?
7. I (am going to) plant an apple tree here.
8. I (

8 am kuch_2016

Here are the verbs in the be going to form:
1. What you (are going to) do with this room? — I (am going to) paint the walls in black and white.
2. The men in the helicopter (are going to) try to help the man in the water.
3. These two men (are going to) cycle across Africa.
4. The man is standing up. He (is going to) make a speech.
5. He (is going to) grow a beard when he leaves school.
6. You (are going to) reserve a seat?
7. I (am going to) plant an apple tree here.
8. I (

8 klas anglijska_mova_kuchma_2016 Here are the verbs in the be going to form:
1. What you (are going to) do with this room? — I (am going to) paint the walls in black and white.
2. The men in the helicopter (are going to) try to help the man in the water.
3. These two men (are going to) cycle across Africa.
4. The man is standing up. He (is going to) make a speech.
5. He (is going to) grow a beard when he leaves school.
6. You (are going to) reserve a seat?
7. I (am going to) plant an apple tree here.
8. I (

Anglijska 8-klas-kuchma-2016 Here are the verbs in the be going to form:
1. What you (are going to) do with this room? — I (am going to) paint the walls in black and white.
2. The men in the helicopter (are going to) try to help the man in the water.
3. These two men (are going to) cycle across Africa.
4. The man is standing up. He (is going to) make a speech.
5. He (is going to) grow a beard when he leaves school.
6. You (are going to) reserve a seat?
7. I (am going to) plant an apple tree here.
8. I (

8 Here are the verbs in the be going to form:
1. What you (are going to) do with this room? — I (am going to) paint the walls in black and white.
2. The men in the helicopter (are going to) try to help the man in the water.
3. These two men (are going to) cycle across Africa.
4. The man is standing up. He (is going to) make a speech.
5. He (is going to) grow a beard when he leaves school.
6. You (are going to) reserve a seat?
7. I (am going to) plant an apple tree here.
8. I (

kinds of permutation.pptx

This document discusses permutation formulas for arranging objects in different scenarios. It covers:
1) Permutations of n objects taken n at a time is n!.
2) Permutations of n objects taken r at a time is n!/(n-r)!.
3) Distinguishable permutations when some objects are alike uses the formula n!/(p!q!r!...).
4) Circular permutations (arranging objects in a circle) is (n-1)!. Examples and solutions are provided to illustrate each type of permutation.

PERMUTATIONS day2.pptx

This document discusses permutations of identical objects and circular permutations. It provides examples of calculating permutations using the formula P=n!/p!q!r! when there are identical objects. Circular permutations are calculated using n!/n or (n-1)! when objects are arranged in a circle. The document includes examples such as seating arrangements, arranging letters in words, and arranging objects on a shelf. Review questions and practice problems are provided to illustrate calculating permutations of identical objects and circular permutations.

Pre-Cal 40S Slides April 20, 2007

This document discusses permutations and combinations related to seating arrangements around a circular table or selecting objects like beads for a necklace or books on a shelf where order matters. It provides examples of calculating the number of arrangements for seating a given number of people or objects in a circle. For problems with additional constraints, like spouses sitting opposite each other, the number of arrangements is reduced.

Pc12 sol c08_review

This document contains examples and solutions for permutations and combinations problems from pre-calculus. It includes 12 problems covering topics like counting the total outcomes of removing coins from bags, determining the number of possible Braille patterns, and finding coefficients in binomial expansions using Pascal's triangle. The document uses formulas, diagrams, and step-by-step workings to explain the solutions.

PERMUTATION-COMBINATION.pdf

This document discusses permutations and combinations. It provides formulas for calculating the number of permutations and combinations of n objects taken r at a time. Examples are given to demonstrate calculating permutations and combinations to solve problems involving arranging objects in different orders or selecting objects without regard to order. Practice problems are included for students to calculate unknown values and solve word problems involving permutations and combinations.

Problem solvingstrategies pp

The data shows the wolf population is decreasing by about 8 wolves every 2 years. If the rate remains constant, the wolf population will drop below 15 in the year 2006.

Permutation

This is about the definition of permutation of n objects taken r at a time, types of permutation, and solving problems involving permutations.

MATHEMATICS 10_4TH QUARTER_PERMUTATION.pptx

MATHEMATICS 10_4TH QUARTER_PERMUTATION.pptx

CYCLIC PERMUTATION.pptx

CYCLIC PERMUTATION.pptx

CIRCULAR PERMUTATION_grade 10_solves problems involving permutations

CIRCULAR PERMUTATION_grade 10_solves problems involving permutations

CIRCULAR PERMUTATION QUESTIONS AND LOGIC

CIRCULAR PERMUTATION QUESTIONS AND LOGIC

Pre-Cal 40S May 6, 2009

Pre-Cal 40S May 6, 2009

Pre-Cal 40S Slides November 28, 2007

Pre-Cal 40S Slides November 28, 2007

8 klas anglijska_mova_kuchma_2016

8 klas anglijska_mova_kuchma_2016

8 am kuch_2016

8 am kuch_2016

8 am kuch_2016

8 am kuch_2016

8 klas anglijska_mova_kuchma_2016

8 klas anglijska_mova_kuchma_2016

Anglijska 8-klas-kuchma-2016

Anglijska 8-klas-kuchma-2016

8

8

kinds of permutation.pptx

kinds of permutation.pptx

PERMUTATIONS day2.pptx

PERMUTATIONS day2.pptx

Pre-Cal 40S Slides April 20, 2007

Pre-Cal 40S Slides April 20, 2007

Pc12 sol c08_review

Pc12 sol c08_review

PERMUTATION-COMBINATION.pdf

PERMUTATION-COMBINATION.pdf

Problem solvingstrategies pp

Problem solvingstrategies pp

Permutation

Permutation

Imagination in Computer Science Research

Conducting exciting academic research in Computer Science

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Conferencia a cargo de D. Ignacio Álvarez Lanzarote dentro del Curso Extraordinario de la Universidad de Zaragoza "Recursos de apoyo en el desarrollo de la competencia digital", que se celebró los días 1, 2 y 3 de julio de 2024.

RDBMS Lecture Notes Unit4 chapter12 VIEW

Description:
Welcome to the comprehensive guide on Relational Database Management System (RDBMS) concepts, tailored for final year B.Sc. Computer Science students affiliated with Alagappa University. This document covers fundamental principles and advanced topics in RDBMS, offering a structured approach to understanding databases in the context of modern computing. PDF content is prepared from the text book Learn Oracle 8I by JOSE A RAMALHO.
Key Topics Covered:
Main Topic : VIEW
Sub-Topic :
View Definition, Advantages and disadvantages, View Creation Syntax, View creation based on single table, view creation based on multiple table, Deleting View and View the definition of view
Target Audience:
Final year B.Sc. Computer Science students at Alagappa University seeking a solid foundation in RDBMS principles for academic and practical applications.
Previous Slides Link:
1. Data Integrity, Index, TAble Creation and maintenance https://www.slideshare.net/slideshow/lecture_notes_unit4_chapter_8_9_10_rdbms-for-the-students-affiliated-by-alagappa-university/270123800
2. Sequences : https://www.slideshare.net/slideshow/sequnces-lecture_notes_unit4_chapter11_sequence/270134792
About the Author:
Dr. S. Murugan is Associate Professor at Alagappa Government Arts College, Karaikudi. With 23 years of teaching experience in the field of Computer Science, Dr. S. Murugan has a passion for simplifying complex concepts in database management.
Disclaimer:
This document is intended for educational purposes only. The content presented here reflects the author’s understanding in the field of RDBMS as of 2024.

What is Rescue Session in Odoo 17 POS - Odoo 17 Slides

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How to Manage Large Scrollbar in Odoo 17 POS

Scroll bar is actually a graphical element mainly seen on computer screens. It is mainly used to optimize the touch screens and improve the visibility. In POS there is an option for large scroll bars to navigate to the list of items. This slide will show how to manage large scroll bars in Odoo 17.

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Our Guide to the July 2024 USPS® Rate Change

Postal Advocate manages the mailing and shipping spends for some of the largest organizations in North America. At this session, we discussed the USPS® July 2024 rate change. Postal Advocate shared all the important information you need to know for this coming rate change that goes into effect on Sunday, July 14, 2024.
We Covered:
-What rates are changing
-How this impacts you
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How to Manage Line Discount in Odoo 17 POS

This slide will cover the management of line discounts in Odoo 17 POS. Using the Line discount approach, we can apply discount for individual product lines.

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- 2. At the end of the lesson, the students should be able to: a. define circular permutation; b.solve problems involving circular permutation; c. relate circular permutations in real-life situations. OBJECTIVES
- 3. CIRCULAR PERMUTATION Circular permutation is the arrangement of objects in a circular manner. It is the total number of ways in which n distinct object can be arranged around a fixed circle defined as, 𝑃 = 𝑛 − 1 !
- 4. Analyze this: Suppose it happens that (1) Jose, (2) Wally and (3) Paolo will visit you in your house, how can you arrange them in a round table if you will prepare them a snack?
- 5. These are 3 possible arrangements if we will arrange them in clockwise position: (1) Jose, (2) Wally, (3) Paolo (2) Wally, (3) Paolo, (1) Jose (3) Paolo, (1) Jose, (2) Wally 1 3 2 (a)
- 6. These are the 3 possible arrangements if we will arrange them in counter clockwise position: (1) Jose, (3) Paolo, (2) Wally (3)Paolo, (2) Wally, (1) Jose (2) Wally, (1) Jose, (3) Paolo 1 3 2 (b)
- 7. Thus, the permutation of n objects arranged in a circle is 𝑃 = (𝑛 − 1)! Wherein: 𝑛 − 𝑖𝑠 𝑡ℎ𝑒 𝑛𝑜. 𝑜𝑓 𝑜𝑏𝑗𝑒𝑐𝑡𝑠 To solve the given problem lets apply the formula Given: 𝑛 = 3 (𝐽𝑜𝑠𝑒, 𝑃𝑎𝑜𝑙𝑜, 𝑊𝑎𝑙𝑙𝑦)
- 8. Solution: 𝑃 = 𝑛 − 1 ! 𝑃 = 3 − 1 ! 𝑃 = 2! 𝑃 = 2 × 1 𝑃 = 2 Therefore, there are 2 possible ways we can arrange Jose, Wally and Paolo if they will seat in a round table.
- 9. a. When clockwise and counter-clockwise orders are different There are two types of circular permutation: b. When clockwise and counter-clockwise orders are the same
- 10. a. When clockwise and counter-clockwise orders are different/ If the clockwise and counter-clockwise orders CAN be distinguished, then the total number of circular permutations of n elements taken all together is 𝑃𝑛 = 𝑛 − 1!
- 11. Example 1: Suppose 7 students are sitting around a circle. Calculate the number of permutations if clockwise and anticlockwise arrangements are different.
- 12. Solution: 𝑃𝑛= 𝑛 − 1! 𝑃𝑛= 7 − 1! 𝑃𝑛 = 6! 𝑃𝑛= 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1 𝑃𝑛= 720 Hence, there are 720 possible arrangements of 7 students around a circle, given the fact that clockwise and anticlockwise arrangements are different.
- 13. Example 2: In how many ways can 8 people be seated at a round table?
- 14. Solution: 𝑃𝑛= 𝑛 − 1! 𝑃𝑛= 8 − 1! 𝑃𝑛= 7! 𝑃𝑛= 7 ⋅ 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1 𝑃𝑛= 5040 Hence, 5040 different combinations are possible of 8 balls in a circle, given the fact that the clockwise and anticlockwise arrangements are different.
- 15. b. Observe the arrangement of different beads in a bracelet, keys on the key rings, and the like. The clockwise and the counter-clockwise orders are not distinguishable.
- 16. So, when clockwise and counter-clockwise orders are the same/ If the clockwise and counter-clockwise orders CANNOT be distinguished, then the total number of circular permutations of n elements taken all together is 𝑃 = 𝑛−1! 2 (without lock/clasp) and
- 17. But if bracelets, key rings, and the like have a lock, then the permutation becomes linear and can be denoted as, 𝑃 = 𝑛! 2 (with lock) where: n - represents the number of objects in a set
- 18. Example 1: In how many ways can 5 different beads be arranged if: a. a bracelet has no lock? b. a bracelet has a lock?
- 19. Solution: a. 𝑃 = 5−1! 2 𝑃 = 4! 2 𝑃 = 24 2 𝑃 = 12 𝑤𝑎𝑦𝑠
- 20. Solution: b. 𝑃 = 5! 2 𝑃 = 120 2 𝑃 = 60 𝑤𝑎𝑦𝑠
- 21. Example 2: Suppose 7 students are sitting around a circle. Calculate the number of permutations if clockwise and anticlockwise arrangements are the same.
- 22. Solution: 𝑃 = 7 − 1! 2 𝑃 = 6! 2 = 720 2 = 360
- 23. Hence, there are 360 permutations if 7 students are sitting around a circle given that the clockwise and anticlockwise arrangements are the same.
- 24. QUIZ TIME!
- 25. Direction: Write it on the 1 whole sheet of paper.
- 26. 1. In how many ways can 10 keys be arranged on a key ring if a key ring has no lock? 2. 11 boy scouts are scattered around a camp fire. How many ways can they be arranged? 3. In how many ways can eight different beads be arranged on a bracelet if a bracelet has a lock? 4. Find the number of different ways that a family of 7 can be seated around a circular table with 7 chairs. 5. 9 students are sitting around a circle. Calculate the number of permutations if clockwise and anticlockwise arrangements are the same.
- 27. 1. How many ways can 10 different colored toy horses be arranged on a merry-go-round? 2. In how many ways can 6 different beads be arranged if: a. a bracelet has no lock? b. a bracelet has a lock?
- 28. In your notebook, try to answer the following questions: 1. President Ferdinand Marcos Jr. together with his 4 Cabinet members is holding a press conference with 6 media reporters. How many different ways can they be seated in a round table if the president and his cabinet members must sit next to each other? 2. Give one example of problems or situations in real life that involve circular permutations. In your example, a. explain the problem or situation. b. solve the problem.
- 29. THANK YOU!