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: 30

Answer

$330$ committees

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 ${}_{n}C_{r}=\displaystyle \frac{n!}{(n-r)!r!}$ -------------- There is no substantial difference in being the first or fourth member of a committee. Order is not important, we deal with combinations. ${}_{11}C_{4}=\displaystyle \frac{11!}{(11-4)!4!}=\frac{11\times 10\times 9\times 8}{1\times 2\times 3\times 4}$ $=11\times 5\times 3\times 2=330$
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