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 $_{7}{{C}_{7}}$.
Here, $ n=7,r=7$.
Put the value of n, r in the above formula. Then:
$\begin{align}
& _{7}{{C}_{7}}=\frac{7!}{\left( 7-7 \right)!7!} \\
& =\frac{7!}{0!7!} \\
& =\frac{1}{0!}
\end{align}$
Since, $0!=1$
So, $\begin{align}
& \frac{1}{0!}=\frac{1}{1} \\
& =1
\end{align}$
Hence, $_{7}{{C}_{7}}=1$