Answer
The required solution is $3024$
Work Step by Step
We know that the representation $_{n}{{P}_{r}}$ implies that the number of possible well-organized arrangements of n items is taken r at a time.
And the number of possible well-organized arrangements of n items taken r at a time can be evaluated as:
$_{n}{{P}_{r}}=\frac{n!}{\left( n-r \right)!}$
And the provided expression is $_{9}{{P}_{4}}$.
Here, $ n=9,r=4$.
Put the value of n, r in the above formula. Then:
$\begin{align}
& _{9}{{P}_{4}}=\frac{9!}{\left( 9-4 \right)!} \\
& =\frac{9!}{5!} \\
& =\frac{9\cdot 8\cdot 7\cdot 6\cdot 5!}{5!}
\end{align}$
Simplify further, $\begin{align}
& \frac{9\cdot 8\cdot 7\cdot 6\cdot 5!}{5!}=9\cdot 8\cdot 7\cdot 6 \\
& =3024
\end{align}$
Hence, $_{9}{{P}_{4}}=3024$
