Pre-Cal 40S Slides April 25, 2008
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This document discusses counting and combinatorics. It introduces fundamental counting principles like the multiplication principle and factorial notation. It provides examples of counting problems like determining the number of ways coins can land on a table in a tree diagram, counting outfits from different numbers of pants and shirts, and seating arrangements of students in vacant seats. Factorial notation is defined as n! = n x (n-1) x (n-2) x ... x 3 x 2 x 1, with examples provided to calculate factorials.
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This document discusses counting rules and methods for determining the number of possible outcomes of an event. It begins by explaining that counting rules are needed when the number of possibilities is too large to list completely, such as when tossing coins and dice. The fundamental counting rule states that if one operation can be done in n1 ways and a second in n2 ways, the combined operations can be done in n1×n2 ways. Permutations refer to arrangements that consider order important, while combinations disregard order. Formulas are provided for calculating permutations and combinations. Examples demonstrate applying these rules and formulas to problems involving arranging objects and selecting subsets of items.
Mathematics prof
Mathematics is the study of quantity, structure, space, and change. Mathematicians seek patterns and establish truth through rigorous logic and deduction from chosen axioms and definitions. The document then provides examples of different types of sequences including geometric sequences defined by multiplying a number each time, arithmetic sequences defined by adding a number each time, and special sequences like triangular and square numbers generated from patterns. It also discusses how to identify if a sequence is arithmetic, geometric, or harmonic based on relationships between terms.
Chapter Five.ppthhjhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
The document provides an overview of elementary probability concepts including:
- Defining probability as the chance of an event occurring and explaining common probability notions.
- Introducing key probability terms like sample space, events, outcomes, and complementary/intersection of events.
- Explaining counting rules like the addition rule, multiplication rule, and how to calculate permutations and combinations.
- Outlining different approaches to defining probability including classical, subjective, axiomatic, and frequency-based definitions.
- Detailing several probability rules like calculating the probability of a union of events and applying the addition rule to non-mutually exclusive events.
Chapter Five.ppthhjhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
The document provides an overview of elementary probability concepts including:
- Defining probability as the chance of an event occurring and explaining common probability notions.
- Introducing key probability terms like sample space, events, outcomes, and complementary/intersection of events.
- Explaining counting rules like the addition rule, multiplication rule, and how to calculate permutations and combinations.
- Outlining different approaches to defining probability including classical, subjective, axiomatic, and frequency-based definitions.
- Detailing several probability rules like calculating the probability of a union of events and applying the addition rule to non-mutually exclusive events.
Counting
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http://www.youtube.com/onlineteaching
Chapter 4: Probability
4. 4: Counting
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Lecture Week 17 which hleps in study for logic and
Lecture Week 17 which hleps in study for logic and
statiscs and probability math college to help student
statiscs and probability math college to help student
Chapter Five.ppthhjhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Chapter Five.ppthhjhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Chapter Five.ppthhjhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Chapter Five.ppthhjhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
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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.
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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.
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Pre-Cal 40S Slides April 25, 2008
- 1. Counting A.K.A. Combinatorics Heeley City Farm 014_edited-1 hopscotch by flickr user incurable_hippie
- 2. In how many ways can 5 people be seated in a straight line?
- 3. A nickel and a quarter and a dime are tossed on a table. Create a tree diagram to determine how many ways these coins can land on the table. (The order in which the coins land doesn't matter; it will next week.)
- 4. The Fundamental Principle of Counting If there are M ways to do a first thing and N ways to do a second thing, then there are M x N ways to do both things. Example: How many outfits can be made from 3 pants and 4 shirts?
- 5. In how many ways can six students be seated in 8 vacant seats?