Answer
$_{12}C_7=792$
Work Step by Step
Using $
_nC_r=\dfrac{n!}{r!\text{ }(n-r)!}
$ or the Combination of $n$ taken $r,$ then
\begin{align*}\require{cancel}
_{12}C_7&=
\dfrac{12!}{7!\text{ }(12-7)!}
\\\\&=
\dfrac{12!}{7!\text{ }5!}
\\\\&=
\dfrac{12(11)(10)(9)(8)(7!)}{7!\text{ }5!}
\\\\&=
\dfrac{12(11)(10)(9)(8)(\cancel{7!})}{\cancel{7!}\text{ }5!}
\\\\&=
\dfrac{12(11)(10)(9)(8)}{5!}
\\\\&=
\dfrac{12(11)(10)(9)(8)}{5(4)(3)(2)(1)}
\\\\&=
\dfrac{12(11)(\cancel{10})(9)(8)}{\cancel5(4)(3)(\cancel2)(1)}
\\\\&=
\dfrac{12(11)(9)(8)}{(4)(3)(1)}
\\\\&=
\dfrac{\cancel{12}(11)(9)(8)}{(\cancel4)(\cancel3)(1)}
\\\\&=
(11)(9)(8)
\\&=
792
.\end{align*}
Hence $
_{12}C_7=792
.$
