# Chapter 11 - Further Topics in Algebra - 11.6 Basics of Counting Theory - 11.6 Exercises - Page 1062: 41

$5040$

#### Work Step by Step

Arrangements $\Rightarrow$ Permutations. $P(n,r)=\displaystyle \frac{n!}{(n-r)!}$. He takes r=7 from n=7 blocks, so $P(7,7)=\displaystyle \frac{7!}{(7-7)!}\qquad$ ... by definition of factorials, $0!=1$ $=7!$ $=7\times 6\times 5\times 4\times 3\times 2\times 1$ = $5040$

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