## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 10 - Section 10.6 - Counting Principles, Permutations, and Combinations - Exercise Set - Page 1103: 3

#### Answer

The required solution is $6720$

#### 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 $_{8}{{P}_{5}}$. Here, $n=8,r=5$. Put the value of n, r in the above formula. Then: \begin{align} & _{8}{{P}_{5}}=\frac{8!}{\left( 8-5 \right)!} \\ & =\frac{8!}{3!} \\ & =\frac{8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3!}{3!} \end{align} And simplify further, \begin{align} & \frac{8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3!}{3!}=8\cdot 7\cdot 6\cdot 5\cdot 4 \\ & =6720 \end{align} Hence, $_{8}{{P}_{5}}=6720$

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