Answer
$495$
Work Step by Step
Using $\left( \array{n\\r} \right)=\dfrac{n!}{r!(n-r)!},$ the given expression, $\left( \array{
12\\4
} \right)$ evaluates to
\begin{array}{l}\require{cancel}
=\dfrac{12!}{4!(12-4)!}
\\\\=
\dfrac{12!}{4!8!}
\\\\=
\dfrac{12(11)(10)(9)(8!)}{4(3)(2)(1)(8!)}
\\\\=
\dfrac{\cancel{12}(11)(\cancel{10}^5)(9)(\cancel{8!})}{\cancel{4(3)}(\cancel{2})(1)(\cancel{8!})}
\\\\=
\dfrac{495}{1}
\\\\=
495
\end{array}
