Answer
$1$
Work Step by Step
Using $C(n,r)=\dfrac{n!}{r!(n-r)!},$ the given expression, $C(
6,0
)$ evaluates to
\begin{array}{l}\require{cancel}
=\dfrac{6!}{0!(6-0)!}
\\\\=
\dfrac{6!}{0!6!}
\\\\=
\dfrac{6!}{(1)(6!)}
\\\\=
\dfrac{\cancel{6!}}{(1)(\cancel{6!})}
\\\\=
1
\end{array}
