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: 46


The number of different ways in which the director can cast the male role is 336.

Work Step by Step

The director will cast 3 male roles from a group of 8 actors. The order in which the actors are chosen matters because Tony, Riff, and Bernardo each have different roles. Thus, we need to find the number of permutations of 8 things taken 3 at a time. Apply the formula, ${}_{n}{{P}_{r}}=\frac{n!}{\left( n-r \right)!}$ Where $ n=8,r=3$ $\begin{align} & {}_{8}{{P}_{3}}=\frac{8!}{\left( 8-3 \right)!} \\ & =\frac{8!}{5!} \end{align}$ Solve further to get: $\begin{align} & _{8}{{P}_{3}}=\frac{8\times 7\times 6\times 5!}{5!} \\ & =8\times 7\times 6 \\ & =336 \end{align}$
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