Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 6 - Section 6.3 - Permutations and Combinations - Exercises - Page 414: 30

Answer

a) 4242 committees with at least 1 woman b) 4221 committees with at least 1 man and 1 woman

Work Step by Step

a) Total people = 9 + 7 = 16 Total committees of 5 members possible = $C$(16,5) = 4368 Committees with only men = $C$(9,5) = 126 Committees with at least 1 woman = Total - only men = 4368 - 126 = 4242 b) committees with only women = $C$(7,5) = 21 Committees with at least 1 man and 1 woman = total - only men - only women = 4368 - 126 - 21 = 4221
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