#### 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$ ...
$=\displaystyle \frac{10\times 9\times 8\times 7\times 6\times 5\times 4\times(3!)}{(3!)}$
$=10\times 9\times 8\times 7\times 6\times 5\times 4$
= $604,800$