College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 9, Counting and Probability - Section 9.1 - Counting - 9.1 Exercises: 13

Answer

$330$

Work Step by Step

RECALL: $C(n, r) = \dfrac{n!}{r!(n-r)!}$ Use the formula above to obtain: $C(11, 4) = \dfrac{11!}{4!(11-4)!} \\C(11, 4) = \dfrac{11!}{4!(7!)} \\C(11, 4) = \dfrac{11(10)(9)(8)(7!)}{4\cdot3\cdot2\cdot1 \cdot 7!}$ Cancel the common factors to obtain: $\require{cancel} \\C(11, 4) = \dfrac{11(10)(9)\cancel{(8)}\cancel{(7!)}}{\cancel{4}\cdot3\cdot\cancel{2}\cdot1 \cdot \cancel{7!}} \\C(11, 4) = \dfrac{11(10)\cancel{(9)}3}{\cancel{3}} \\C(11, 4) = 330$
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