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: 58

Answer

The number of ways to select 8 books out of 40 books is $76,904,685$.

Work Step by Step

We know that: ${}_{n}{{C}_{r}}=\frac{n!}{r!\left( n-r \right)!}$ So, from the information, $\begin{align} & n=40 \\ & r=8 \end{align}$ Then, we know that to find the number of combinations of 40 things taken 8 at a time, we applying the above formula: $\begin{align} & {}_{40}{{C}_{8}}=\frac{40!}{8!\left( 40-8 \right)!} \\ & =\frac{40!}{8!32!} \\ & =\frac{40\times 39\times 38\times 37\times 36\times 35\times 34\times 33\times 32!}{8!\times 32!} \\ & =76,904,685 \end{align}$ Thus, the number of ways to select 8 books out of 40 books are $76,904,685$.
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