Chapter 7 - Section 7.4 - The Binomial Theorem - 7.4 Exercises - Page 664: 15

$4,950$

Using $_nC_r=\dfrac{n!}{r!(n-r)!},$ the given expression, $ _{100}C_{98} $ evaluates to \begin{array}{l}\require{cancel} =\dfrac{100!}{98!(100-98)!} \\\\= \dfrac{100!}{98!2!} \\\\= \dfrac{100(99)(98!)}{98!(2)(1)} \\\\= \dfrac{\cancel{100}^{50}(99)(\cancel{98!})}{\cancel{98!}(\cancel{2})(1)} \\\\= \dfrac{4950}{1} \\\\= 4,950 \end{array}