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: 80


There are 1140 ways of selecting three CDs from a set of 20 CDs

Work Step by Step

We know that the order in which the three CD’s are selected does not make a difference since all would be taken for the vacation at the same time. Since the order of the arrangement does not make a difference, we solve the problem with combinations.. The three CD’s are to be selected from a group of twenty CD’s. So, $ n=20,r=3$. Hence, $\begin{align} & _{20}{{C}_{3}}=\frac{20!}{3!\left( 20-3 \right)!} \\ & =\frac{20!}{3!17!} \\ & =\frac{20\times 19\times 18\times 17!}{6\times 17!} \\ & =1140 \end{align}$
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