## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 10 - Section 10.6 - Counting Principles, Permutations, and Combinations - Exercise Set - Page 1103: 2

#### Answer

The required solution is $210$

#### 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: $_{n}{{P}_{r}}=\frac{n!}{\left( n-r \right)!}$ The provided expression is $_{7}{{P}_{3}}$. Here, $n=7,r=3$. Put the value of n, r in the above formula. Then: \begin{align} & _{7}{{P}_{3}}=\frac{7!}{\left( 7-3 \right)!} \\ & =\frac{7!}{4!} \\ & =\frac{7\cdot 6\cdot 5\cdot 4!}{4!} \end{align} And simplify further, \begin{align} & \frac{7\cdot 6\cdot 5\cdot 4!}{4!}=7\cdot 6\cdot 5 \\ & =210 \end{align} Hence, $_{7}{{P}_{3}}=210$

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