Answer
The required solution is $330$
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 $_{11}{{C}_{4}}$.
Here, $ n=11,r=4$.
Put the value of n, r in the above formula. Then:
$\begin{align}
& _{11}{{C}_{4}}=\frac{11!}{\left( 11-4 \right)!4!} \\
& =\frac{11!}{7!4!} \\
& =\frac{11\cdot 10\cdot 9\cdot 8\cdot 7!}{7!\cdot 4\cdot 3\cdot 2\cdot 1}
\end{align}$
Simplifying further, $\begin{align}
& \frac{11\cdot 10\cdot 9\cdot 8\cdot 7!}{7!\cdot 4\cdot 3\cdot 2\cdot 1}=\frac{11\cdot 10\cdot 9\cdot 8}{4\cdot 3\cdot 2\cdot 1} \\
& =\frac{7920}{24} \\
& =330
\end{align}$
Hence, $_{11}{{C}_{4}}=330$
