College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 10 - Section 10.2 - Permutations and Combinations - 10.2 Assess Your Understanding - Page 696: 62

Answer

See below.

Work Step by Step

If we want to choose $k$ elements out of $n$ disregarding the order, not allowing repetition, we can do this in $_{n}C_k=\frac{n!}{(n-k)!k!}$ ways. The order doesn't matter here in the set of players, thus we have to use combinations. Thus $_{2}C_{1}(center)_{3}C_{2}(guards)_{12-2-3}C_{2}(forward)=2\cdot3\cdot21=126$
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