# Chapter 11

## Chapter 11

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##### Presentation Transcript

2. Chapter 11: Counting Methods 11.1 Counting by Systematic Listing 11.2 Using the Fundamental Counting Principle 11.3 Using Permutations and Combinations 11.4 Using Pascal’s Triangle 11.5 Counting Problems Involving “Not” and “Or” © 2008 Pearson Addison-Wesley. All rights reserved

5. Uniformity Criterion for Multiple-Part Tasks A multiple-part task is said to satisfy the uniformity criterion if the number of choices for any particular part is the same no matter which choices were selected for the previous parts. © 2008 Pearson Addison-Wesley. All rights reserved

6. Fundamental Counting Principle When a task consists of k separate parts and satisfies the uniformity criterion, if the first part can be done in n1 ways, the second part can be done in n2 ways, and so on through the kth part, which can be done in nk ways, then the total number of ways to complete the task is given by the product © 2008 Pearson Addison-Wesley. All rights reserved

8. Example: Two-Digit Numbers with Restrictions How many two-digit numbers that do not contain repeated digits can be made from the set {0, 1, 2, 3, 4, 5} ? Solution There are 5(5) = 25 two-digit numbers. © 2008 Pearson Addison-Wesley. All rights reserved

9. Example: Two-Digit Numbers with Restrictions How many ways can you select two letters followed by three digits for an ID? Solution There are 26(26)(10)(10)(10) = 676,000 IDs possible. © 2008 Pearson Addison-Wesley. All rights reserved

10. Factorials For any counting number n, the product of all counting numbers from n down through 1 is called n factorial, and is denoted n!. © 2008 Pearson Addison-Wesley. All rights reserved