## Precalculus (6th Edition) Blitzer

The required solution is $5040$
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: $_{n}{{P}_{r}}=\frac{n!}{\left( n-r \right)!}$ andthe provided expression is $_{10}{{P}_{4}}$. Here, $n=10,r=4$. Put the value of n, r in the above formula. Then: \begin{align} & _{10}{{P}_{4}}=\frac{10!}{\left( 10-4 \right)!} \\ & =\frac{10!}{6!} \\ & =\frac{10\cdot 9\cdot 8\cdot 7\cdot 6!}{6!} \end{align} Simplifying further, \begin{align} & \frac{10\cdot 9\cdot 8\cdot 7\cdot 6!}{6!}=10\cdot 9\cdot 8\cdot 7 \\ & =5040 \end{align} Hence, $_{10}{{P}_{4}}=5040$