Answer
$_4C_4=1$
Work Step by Step
Using $
_nC_r=\dfrac{n!}{r!\text{ }(n-r)!}
$ or the Combination of $n$ taken $r,$ the given expression, $
_4C_4
,$ is equivalent to
\begin{align*}\require{cancel}
&
\dfrac{4!}{4!\text{ }(4-4)!}
\\\\&=
\dfrac{4!}{4!\text{ }0!}
\\\\&=
\dfrac{4!}{4!\text{ }1}
&\text{(use }0!=1)
\\\\&=
\dfrac{\cancel{4!}}{\cancel{4!}\text{ }1}
\\\\&=
1
.\end{align*}
Hence, $
_4C_4=1
.$
