Answer
$120$
Work Step by Step
Using $n!=n(n-1)(n-2)\cdot...(3)(2)(1),$ the given expression, $
\dfrac{10!}{7!\text{ }3!}
,$ simplifies to
\begin{align*}\require{cancel}
&
\dfrac{10(9)(8)(7!)}{7!\text{ }3(2)(1)}
\\\\&=
\dfrac{10(9)(8)(\cancel{7!})}{\cancel{7!}\text{ }3(2)(1)}
\\\\&=
\dfrac{10(\cancel9^3)(8)}{\cancel3(2)(1)}
\\\\&=
\dfrac{10(3)(\cancel8^4)}{\cancel2(1)}
\\\\&=
10(3)(4)
\\&=
120
.\end{align*}
Hence, the given expression evaluates to $
120
.$
