Answer
$15,504$
Work Step by Step
Using $_nC_r=\dfrac{n!}{r!(n-r)!},$ the given expression, $
_{20}C_{5}
,$ evaluates to
\begin{array}{l}\require{cancel}
=\dfrac{20!}{5!(20-5)!}
\\\\=
\dfrac{20!}{5!15!}
\\\\=
\dfrac{20(19)(18)(17)(16)(15!)}{5(4)(3)(2)(1)(15!)}
\\\\=
\dfrac{\cancel{20}(19)(\cancel{18}^3)(17)(16)(\cancel{15!})}{\cancel{5(4)}\cancel{(3)(2)}(1)(\cancel{15!})}
\\\\=
\dfrac{15504}{1}
\\\\=
15,504
\end{array}
