Answer
The required solution is $126$
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 $_{9}{{C}_{5}}$.
Here, $ n=9,r=5$.
Put the value of n, r in the above formula. Then:
$\begin{align}
& _{9}{{C}_{5}}=\frac{9!}{\left( 9-5 \right)!5!} \\
& =\frac{9!}{4!5!} \\
& =\frac{9\cdot 8\cdot 7\cdot 6\cdot 5!}{4\cdot 3\cdot 2\cdot 1\cdot 5!}
\end{align}$
And simplify further, $\begin{align}
& \frac{9\cdot 8\cdot 7\cdot 6\cdot 5!}{4\cdot 3\cdot 2\cdot 1\cdot 5!}=\frac{9\cdot 8\cdot 7\cdot 6}{4\cdot 3\cdot 2\cdot 1} \\
& =\frac{3024}{24} \\
& =126
\end{align}$
Hence, $_{9}{{C}_{5}}=126$