Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 11 - Counting Methods and Probability Theory - 11.2 Permutations - Exercise Set 11.2 - Page 701: 35



Work Step by Step

Permutations Formula, page 698: The number of permutations possible if $r$ items are taken from $n$ items is ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$. Factorial Notation, page 696: $n!=n(n-1)(n-2)\cdots(3)(2)(1)$ and, by definition, $0!=1$ ------------------ ${}_{8}P_{5}=\displaystyle \frac{8!}{(8-5)!}=\frac{8!}{3!}$ $=\displaystyle \frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{3\times 2\times 1}$ $=8\times 7\times 6\times 5\times 4=6720$
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