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 - Page 707: 37


735 ways

Work Step by Step

Committee members are chosen with no importance of order of choice, so we deal with combinations. We have a sequence of selections in which we choose 1. ... 4 men out of a group of 7 ... in ${}_{7}C_{4}$ ways 2. ... 5 women out of a group of 7 ... in ${}_{7}C_{5}$ ways By the Fundamental Counting Principle, Total ways= ${}_{7}C_{4}\cdot {}_{7}C_{5}$ ${}_{7}C_{4}=\displaystyle \frac{7!}{(7-4)!4!}=\frac{7\times 6\times 5}{1\times 2\times 3}=35$ ${}_{7}C_{5}=\displaystyle \frac{7!}{(7-5)!5!}=\frac{7\times 6}{1\times 2}=21$ Total = 35$\times$21 = 735 ways
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