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: 42



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
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.