Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.5 The Binomial Theorem - 12.5 Assess Your Understanding - Page 836: 10



Work Step by Step

Recall: ${n\choose j}=\dfrac{n!}{(n-j)!j!}$. Hence, \begin{align*} \require{cancel} {100\choose 98}&=\dfrac{100!}{(100-98)!98!}\\ &=\dfrac{100!}{2!98!}\\ &=\dfrac{100\cdot99\cdot98!}{2!98!}\\ &=\dfrac{100\cdot99\cdot\cancel{98!}}{2\cdot1\cdot\cancel{98!}}\\ &=\dfrac{9900}{2}\\ &=4950\end{align*}
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