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: 41

Answer

720

Work Step by Step

A permutation from a group of items occurs when no item is used more than once and the order of arrangement makes a difference. The number of permutations possible if $r$ items are taken from $n$ items is ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$. ---------------- Order of selecting members to office is important, as it makes a difference whether member A has been chosen to be 1. the president, 2. the vice president, or 3. the secretary-treasurer. Conclusion: we can use the formula ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$. where r=3 members are taken from n=10 members. ${}_{11}P_{3}=\displaystyle \frac{10!}{8!}=10\times 9\times 8=720 $ways
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