Answer
$\dfrac{12!}{6!\text{ }3!}=110880$
Work Step by Step
Using the factorial of a number which is given by $n!=n(n-1)(n-2)...(3)(2)(1),$ the given expression, $
\dfrac{12!}{6!\text{ }3!}
,$ is equivalent to
\begin{align*}\require{cancel}
&
\dfrac{12(11)(10)(9)(8)(7)(6!)}{6!\text{ }3(2)(1)}
\\\\&=
\dfrac{12(11)(10)(9)(8)(7)(\cancel{6!})}{\cancel{6!}\text{ }3(2)(1)}
\\\\&=
\dfrac{12(11)(10)(9)(8)(7)}{3(2)(1)}
\\\\&=
\dfrac{12(11)(10)(\cancel9^3)(8)(7)}{\cancel3(2)(1)}
\\\\&=
\dfrac{12(11)(10)(3)(\cancel8^4)(7)}{(\cancel2)(1)}
\\\\&=
12(11)(10)(3)(4)(7)
\\&=
110880
.\end{align*}
Hence, $
\dfrac{12!}{6!\text{ }3!}=110880
.$
