Precalculus (6th Edition) Blitzer

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

Chapter 10 - Review Exercises - Page 1126: 79


The number of ways four actors can be selected is 4845 ways

Work Step by Step

We know that the order in which the four actors are selected does not make a difference as the designation for all the four actors would be the same. The ordered arrangement in which the order of the arrangement does not make a difference is solved using the concepts of combinations. The four actors are to be selected from a group of twenty actors. So, $ n=20,r=4$. Hence, $\begin{align} & _{20}{{C}_{4}}=\frac{20!}{4!\left( 20-4 \right)!} \\ & =\frac{20!}{4!16!} \\ & =\frac{20\times 19\times 18\times 17\times 16!}{24\times 16!} \\ & =4845 \end{align}$
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