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: 10

Answer

$4,950$

Work Step by Step

RECALL: ${n}\choose{k}$$=\dfrac{n!}{k!(n-k)!}$ Use the formula above to obtain: ${100}\choose{98}$$\require{cancel} \\=\dfrac{100!}{98!(100-98)!} \\=\dfrac{100!}{98!2!} \\=\dfrac{100\cdot 99 \cdot 98!}{98! (2\cdot 1)} \\=\dfrac{\cancel{100}^{50}\cdot 99 \cdot \cancel{98!}}{\cancel{98!} (\cancel{2}\cdot 1)} \\=4950$
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