Isye 2027

# Someone selects two at random all possibilities being

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Unformatted text preview: size k of a set of n distinct objects (with the order not mattering) is given by n(n−1)···(n−k+1) n . This is equal to (n−k!)!k! , and is called “n choose k ,” and is written as the binomial k! n coeﬃcient, n = (n−k!)!k! . k It is useful to keep in mind that n k = n n−k and that k n k = terms n(n − 1) · · · (n − k + 1) . k! For example, 8 and 8 are both equal to 8·7·6 = 56, which is also equal to 8·7·6·5·4 . 3 5 3·2·1 5·4·3·2·1 Note that (a + b)2 = a2 + 2ab + b2 and (a + b)3 = a3 + 3a2 b + 3ab2 + b3 . In general, n (a + b)n = k=0 n k n−k ab . k (1.5) Equation (1.5) follows by writing (a + b)n = (a + b)(a + b) · · · (a + b), and then noticing that the n factors coeﬃcient of ak bn−k in (a + b)n is the number of ways to select k out of the n factors from which to select a. 16 1.4 CHAPTER 1. FOUNDATIONS Probability experiments with equally likely outcomes This section presents more examples of counting, and related probability experiments such that all outcomes are equally likely. Example 1.4.1 Suppose there are nine socks loose in a drawer in a dark room which are identical except six are orange a...
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## This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.

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