Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 11824 - 11.6 - Counting Principles - 11.6 Exercises - Page 824: 60


44,186,942,677,323,600 different committees.

Work Step by Step

The order in which the senators are selected is not important. It is a combination of 14 senators from a group of 100 senators. $_{100}C_{14}=\frac{100!}{(100-14)!~14!}=\frac{100\times99\times98\times97\times96\times95\times94\times93\times92\times91\times90\times89\times88\times87\times86!}{86!~14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}=44,186,942,677,323,600$
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