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Unformatted text preview: size k of a set of n distinct objects (with the order not mattering) is given by
. This is equal to (n−k!)!k! , and is called “n choose k ,” and is written as the binomial
coeﬃcient, n = (n−k!)!k! .
It is useful to keep in mind that n
k = n
n−k and that
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 .
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
k (1.5) Equation (1.5) follows by writing (a + b)n = (a + b)(a + b) · · · (a + b), and then noticing that the
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.
- Spring '08
- The Land