## Precalculus (6th Edition) Blitzer

The required solution is $3024$
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, $_{9}{{P}_{4}}=3024$