Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 10 - Section 10.6 - Counting Principles, Permutations, and Combinations - Exercise Set - Page 1104: 47


The number of different ways to line up the bands to perform at a benefit concert is 15120.

Work Step by Step

We need to choose 5 bands from a group of 9 bands. The order in which the bands are chosen matters because one band can perform only once. Therefore, we need to find the number of permutations of 9 things taken 5 at a time. We apply the formula, ${}_{n}{{P}_{r}}=\frac{n!}{\left( n-r \right)!}$ Where $ n=9,r=5$ $\begin{align} & {}_{9}{{P}_{5}}=\frac{9!}{\left( 9-5 \right)!} \\ & =\frac{9!}{4!} \end{align}$ Solve further to get, $\begin{align} & {}_{9}{{P}_{5}}=\frac{9\times 8\times 7\times 6\times 5\times 4!}{4!} \\ & =9\times 8\times 7\times 6\times 5 \\ & =15120 \end{align}$
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