Answer
The required solution is $1$
Work Step by Step
We know that the representation $_{n}{{C}_{r}}$ counts the number of assortments of n items taken r at a time.
And the number of assortment of n items taken r at a time can be evaluated as:
$_{n}{{C}_{r}}=\frac{n!}{\left( n-r \right)!r!}$
And the provided expression is $_{6}{{C}_{0}}$.
Here, $ n=6,r=0$.
Put the value of n, r in the above formula. Then, $\begin{align}
& _{6}{{C}_{0}}=\frac{6!}{\left( 6-0 \right)!0!} \\
& =\frac{6!}{6!0!} \\
& =\frac{1}{0!}
\end{align}$
Since, $0!=1$
So, $\begin{align}
& \frac{1}{0!}=\frac{1}{1} \\
& =1
\end{align}$
Hence, $_{6}{{C}_{0}}=1$
