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

$4950$

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*}