Answer
$45$
Work Step by Step
Using $\left( \array{n\\r} \right)=\dfrac{n!}{r!(n-r)!},$ the given expression, $\left( \array{
10\\2
} \right)$ evaluates to
\begin{array}{l}\require{cancel}
=\dfrac{10!}{2!(10-2)!}
\\\\=
\dfrac{10!}{2!8!}
\\\\=
\dfrac{10(9)(8!)}{2(1)(8!)}
\\\\=
\dfrac{\cancel{10}^5(9)(\cancel{8!})}{\cancel{2}(1)(\cancel{8!})}
\\\\=
\dfrac{45}{1}
\\\\=
45
\end{array}
