## Thinking Mathematically (6th Edition)

Published by Pearson

# Chapter 11 - Counting Methods and Probability Theory - 11.2 Permutations - Exercise Set 11.2: 42

210

#### 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 director A has been chosen to be 1. the president, 2. the vice president, 3. the secretary, or 4. the treasurer. Conclusion: we can use the formula ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$. where r=4 members are taken from n=7 members. ${}_{7}P_{4}=\displaystyle \frac{7!}{3!}=7\times 6\times 5=210$ways

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