College Algebra (10th Edition)

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

Chapter 9 - Section 9.5 - The Binomial Theorem - 9.5 Assess Your Understanding: 8

Answer

$36$

Work Step by Step

RECALL: ${n}\choose{k}$$=\dfrac{n!}{k!(n-k)!}$ Use the formula above to obtain: ${9}\choose{7}$$\require{cancel} \\=\dfrac{9!}{7!(9-7)!} \\=\dfrac{9!}{7!2!} \\=\dfrac{9\cdot 8 \cdot 7!}{7! (2\cdot 1)} \\=\dfrac{9\cdot \cancel{8}^4 \cdot \cancel{7!}}{\cancel{7!} (\cancel{2}\cdot 1)} \\=36$
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