## Precalculus (6th Edition)

Published by Pearson

# Chapter 11 - Further Topics in Algebra - 11.6 Basics of Counting Theory - 11.6 Exercises - Page 1062: 46

#### Answer

$604,800$

#### Work Step by Step

Arrangements $\rightarrow$ Permutations.$P(n,r)=\displaystyle \frac{n!}{(n-r)!}$. Arranging r=$7$ from n=$10$ rats, $P(10,7)=\displaystyle \frac{10!}{(10-7)!}\qquad$ ... $=\displaystyle \frac{10\times 9\times 8\times 7\times 6\times 5\times 4\times(3!)}{(3!)}$ $=10\times 9\times 8\times 7\times 6\times 5\times 4$ = $604,800$

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