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College Algebra Exam Review 48

# College Algebra Exam Review 48 - 58 1 ALGEBRAIC THEMES Then...

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58 1. ALGEBRAIC THEMES Then arrange the first 2 (in D 2 ways) and the last n 2 (in .n 2/Š ways). This strange process for building permutations gives the formula D n 2 2Š .n 2/Š : Now dividing by 2Š .n 2/Š gives n 2 D 2Š.n 2/Š D n.n 1/ 2 : The virtue of this argument is that it remains valid if 2 is replaced by any k , 0 k n . So we have the following: Proposition 1.9.2. Let n be a natural number and let k be an integer in the range 0 k n . Let n k denote the number of k -element subsets of an n -element set. Then n k D kŠ.n k/Š : We extend the definition by declaring
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