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: 23

Answer

609,638,400 ways to them to stand in a line when no two women are adjacent.

Work Step by Step

First let us make all the men stand in a line. The ways in which this could be done = 8! Then we let women stand in places where there is always a man between them. We have 9 places where women can go. So the arrangement is given by $C$(9,5), as we have 9 spots and 5 women. Women can interchange their position in 5! ways So total arrangements are given by 8!$\times$$C$(9,5)$\times$5! = 609,638,400
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