Answer
The required solution is $1$
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 $_{8}{{P}_{0}}$.
Here, $ n=8,r=0$.
Put the value of n, r in the above formula. Then:
$\begin{align}
& _{8}{{P}_{0}}=\frac{8!}{\left( 8-0 \right)!} \\
& =\frac{8!}{8!} \\
& =1
\end{align}$
Hence, $_{8}{{P}_{0}}=1$
