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: 33

Answer

$24,310$ groups

Work Step by Step

A combination from a group of items occurs when no item is used more than once and the order of items makes no difference. The number of combinations possible if $r$ items are taken from $n$ items is ${}_{n}C_{r}=\displaystyle \frac{n!}{(n-r)!r!}$ -------------- When selecting children to drive, it is unimportant which is selected first, second,..., or eighth. Order is not important, we deal with combinations. ${}_{17}C_{8}=\displaystyle \frac{17!}{(17-8)!8!}$ $=\displaystyle \frac{17\times 16\times 15\times 14\times 13\times 12\times 11\times 10}{1\times 2\times 3\times 4\times 5\times 6\times 7\times 8}$ $=\displaystyle \frac{17\times 1\times 1\times 1\times 13\times 1\times 11\times 10}{1\times 1\times 1\times 1\times 1\times 1\times 1\times 1}$ $=24,310$
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