#### Answer

210

#### Work Step by Step

A permutation from a group of items occurs when no item is used more than once and the order of arrangement makes a difference.
The number of permutations possible if $r$ items are taken from $n$ items is
${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$.
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Order of selecting members to office is important,
as it makes a difference whether director A has been chosen to be
1. the president,
2. the vice president,
3. the secretary, or
4. the treasurer.
Conclusion: we can use the formula ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$.
where r=4 members are taken from n=7 members.
${}_{7}P_{4}=\displaystyle \frac{7!}{3!}=7\times 6\times 5=210 $ways