Answer
$560$
Work Step by Step
Using $\left( \array{n\\r} \right)=\dfrac{n!}{r!(n-r)!},$ the given expression, $\left( \array{
16\\3
} \right)$ evaluates to
\begin{array}{l}\require{cancel}
=\dfrac{16!}{3!(16-3)!}
\\\\=
\dfrac{16!}{3!13!}
\\\\=
\dfrac{16(15)(14)(13!)}{3(2)(1)(13!)}
\\\\=
\dfrac{16(\cancel{15}^5)(\cancel{14}^7)(\cancel{13!})}{\cancel{3}(\cancel{2})(1)(\cancel{13!})}
\\\\=
\dfrac{560}{1}
\\\\=
560
\end{array}
