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: 7

Answer

$21$

Work Step by Step

RECALL: ${n}\choose{k}$$=\dfrac{n!}{k!(n-k)!}$ Use the formula above to obtain: ${7}\choose{5}$$\require{cancel} \\=\dfrac{7!}{5!(7-5)!} \\=\dfrac{7!}{5!2!} \\=\dfrac{7\cdot 6 \cdot 5\cdot 4\cdot 3 \cdot 2 \cdot 1}{(5\cdot4\cdot 3\cdot 2 \cdot 1) (2 \cdot 1)} \\=\dfrac{7\cdot \cancel{6}^3 \cdot \cancel{5\cdot 4\cdot 3 \cdot 2 \cdot 1}}{\cancel{(5\cdot4\cdot 3\cdot 2 \cdot 1)} (\cancel{2} \cdot 1)} \\=21$
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