Answer
$6,435$
Work Step by Step
Using $\left( \array{n\\r} \right)=\dfrac{n!}{r!(n-r)!},$ the given expression, $\left( \array{
15\\8
} \right)$ evaluates to
\begin{array}{l}\require{cancel}
=\dfrac{15!}{8!(15-8)!}
\\\\=
\dfrac{15!}{8!7!}
\\\\=
\dfrac{15(14)(13)(12)(11)(10)(9)(8!)}{8!(7)(6)(5)(4)(3)(2)(1)}
\\\\=
\dfrac{15(\cancel{14}^2)(13)(\cancel{12}^2)(11)(\cancel{10}^2)(\cancel{9}^3)(\cancel{8!})}{\cancel{8!}(\cancel{7})(\cancel{6})(\cancel{5})(4)(\cancel{3})(2)(1)}
\\\\=
\dfrac{15(\cancel{2})(13)(\cancel{2})(11)(\cancel{2})(3)}{(\cancel{4})(\cancel{2})(1)}
\\\\=
\dfrac{6435}{1}
\\\\=
6,435
\end{array}
