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: 12

Answer

$36$

Work Step by Step

RECALL: $C(n, r) = \dfrac{n!}{r!(n-r)!}$ Use the formula above to obtain: $C(9, 2) = \dfrac{9!}{2!(9-2)!} \\C(9, 2) = \dfrac{9!}{2!(7!)} \\C(9, 2) = \dfrac{9(8)(7!)}{2 \cdot 1(7!)}$ Cancel the common factors to obtain: $\require{cancel} \\C(9, 2) = \dfrac{9\cancel{(8)}4\cancel{(7!)}}{\cancel{2 \cdot 1}\cancel{(7!)}} \\C(9, 2) = 36$
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