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Unformatted text preview: Counting, Permutations, & Combinations A counting problem asks “how many ways” some event can occur. Ex. 1: How many threeletter codes are there using letters A, B, C, and D if no letter can be repeated? • One way to solve is to list all possibilities. Ex. 2: An experimental psychologist uses a sequence of two food rewards in an experiment regarding animal behavior. These two rewards are of three different varieties. How many different sequences of rewards are there if each variety can be used only once in each sequence? Next slide a b c c c b b a a • Another way to solve is a factor tree where the number of end branches is your answer. Fundamental Counting Principle Suppose that a certain procedure P can be broken into n successive ordered stages, S 1 , S 2, . . . S n, and suppose that S 1 can occur in r 1 ways. S 2 can occur in r 2 ways. S n can occur in r n ways. Then the number of ways P can occur is n r r r ⋅ ⋅ ⋅ ⋅ 2 1 Ex. 2: An experimental psychologist uses a sequence of two food rewards in an...
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This note was uploaded on 12/09/2011 for the course STATS 221 taught by Professor Nielson during the Fall '10 term at BYU.
 Fall '10
 Nielson
 Counting

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