Main Goals for Chapter 11 and 12

• To become familiar with different ways to make systematic lists
• To become familiar with the Fundamental Counting Principle
• To understand what a permutation of n objects is and what a combination of n objects is, and what the difference between them is
• To understand how Pascal's triangle can be used for counting
• To understand the binomial theorem
• To understand counting principles for "not" and "or"
• To understand basic probability properties

Section 11.1 Counting by Systematic Listing. Key Ideas: different ways to make lists: tables, tree diagrams, listing labels, etc. Sample exercises (pages 635-637): odd 1-43, 53, 55, 57

Section 11.2  Using the Fundamental Counting Principle.  Key Ideas: uniformity criterion for multi-part tasks, Fundamental Counting Principle (FCP), factorial (n!), arrangements of n objects.  Sample exercises (pages 644-666): 1-23 (odd), 31, 33, 39, 41, 43, 45, 51, 55

Section 11.3  Using Permutations and Combinations.  Key Ideas: permutations (formula, guidelines for when to use permutations), combinations (formula and guidelines), how to tell if something requires a permutation or a combination.  Sample exercises (pages 655-658): 17-51 (odd).

Section 11.4. Using Pascal's Triangle and the Binomial Theorem.  Key Ideas: how the entries of Pascal's triangle relate to combinations, the Binomial Theorem.  Sample exercises (pages 662-664): 1-27 (odd), 41, 43, 45

Section 11.5  Counting Problems Involving "Not" and "Or".  Key Ideas: general additive counting principle.   Sample exercises (pages 669-670): 3-41 (odd), 43, 44, 45, 46, 47, 48

Section 12.1 Basic Concepts.  Key Ideas: theoretical probability formula, odds.  Sample exercises (pages 681-683): 1, 3, 9, 11, 45, 47, 51, 53

Section 12.2 Events involving "Not" and "Or".  Key Ideas: properties of probability, using complements, general addition rule.  Sample exercises (pages 689-691): 5, 7, 11, 13, 15, 17, 19, 23, 25

Chapter 11 and 12 Slides

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last updated April 10, 2012