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: 6

Answer

$35$

Work Step by Step

RECALL: ${n}\choose{k}$$=\dfrac{n!}{k!(n-k)!}$ Use the formula above to obtain: ${7}\choose{3}$$\require{cancel}=\dfrac{7!}{3!(7-3)!}=\dfrac{7!}{3!4!}=\dfrac{7\cdot 6 \cdot 5\cdot 4\cdot 3 \cdot 2 \cdot 1}{(3\cdot 2 \cdot 1) (4\cdot 3 \cdot 2 \cdot 1)}=\dfrac{7\cdot \cancel{6} \cdot 5\cdot \cancel{4\cdot 3 \cdot 2 \cdot 1}}{(\cancel{3\cdot 2} \cdot 1) \cancel{(4\cdot 3 \cdot 2 \cdot 1)}}=35$
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