## Precalculus (6th Edition)

$5040$ different arrangements.
"...in a row..." - order matters. Permutations. We are taking r=7 from n=7 portraits, $P(n,r)=\displaystyle \frac{n!}{(n-r)!}$. $P(7,7)=\displaystyle \frac{7!}{(7-7)!}\qquad$ ... 0!=1, by definition $P(7,7)=7!$ $=7\times 6\times 5\times 4\times 3\times 2\times 1$ = $5040$ different arrangements.