Statistics: Informed Decisions Using Data (4th Edition)

Published by Pearson
ISBN 10: 0321757270
ISBN 13: 978-0-32175-727-2

Chapter 5 - Section 5.5 - Assess Your Understanding - Applying the Concepts - Page 306: 50

Answer

$293,930$ different committee structures.

Work Step by Step

The order in which the members are selected does not matter and no member can be selected more than once. Combination of 21 distinct members taken 9 at a time: $_{21}C_{9}=\frac{21!}{9!(21-9)!}=\frac{21!}{9!\times12!}$ But, $21!=21\times20\times19\times18\times17\times16\times15\times14\times13\times(12\times11\times10\times ... \times3\times2\times1)=21\times20\times19\times...\times12!$ $_{21}C_{9}=\frac{21\times20\times19\times18\times17\times16\times15\times14\times13\times12!}{9!\times12!}=\frac{21\times20\times19\times18\times17\times16\times15\times14\times13}{9\times8\times7\times\times5\times4\times3\times2\times1}=293,930$
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