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: 11

Answer

$56$

Work Step by Step

RECALL: $C(n, r) = \dfrac{n!}{r!(n-r)!}$ Use the formula above to obtain: $C(8, 3) = \dfrac{8!}{3!(8-3)!} \\C(8, 3) = \dfrac{8!}{3!(5!)} \\C(8, 3) = \dfrac{8(7)(6)(5!)}{3\cdot 2 \cdot 1(5!)}$ Cancel the common factors to obtain: $\require{cancel} \\C(8, 3) = \dfrac{8(7)\cancel{(6)}(\cancel{5!})}{\cancel{3\cdot 2 \cdot 1}\cancel{(5!)}} \\C(8, 3) = 56$
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