Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 11 - Counting Methods and Probability Theory - 11.3 Combinations - Exercise Set 11.3: 42

Answer

$76,904,685$ ways

Work Step by Step

The order in which the books are chosen is not important. Combinations, ${}_{n}C_{r}=\displaystyle \frac{n!}{(n-r)!r!}$ ${}_{40}C_{8}=\displaystyle \frac{40!}{(40-8)!8!}$ $=\displaystyle \frac{40\times 39\times 38\times 37\times 36\times 35\times 34\times 33}{1\times 2\times 3\times 4\times 5\times 6\times 7\times 8}$ $=\displaystyle \frac{1\times 39\times 19\times 37\times 1\times 5\times 17\times 33}{1\times 1\times 1\times 1\times 1\times 1\times 1\times 1}$ $= 76,904,685$
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