select the correct answer. an art gallery wants to display 4 pieces of art in the front window. if there are…

Answer:

C. 1,680

Explanation:

Step1: Identify the permutation formula

The formula for permutations is $P(n,r)=\frac{n!}{(n - r)!}$, where $n$ is the total number of items and $r$ is the number of items to be chosen.

Step2: Substitute values

Here, $n = 8$ and $r=4$. So $P(8,4)=\frac{8!}{(8 - 4)!}=\frac{8!}{4!}$.

Step3: Expand factorials

$8! = 8\times7\times6\times5\times4!$, so $\frac{8!}{4!}=\frac{8\times7\times6\times5\times4!}{4!}$.

Step4: Simplify

The $4!$ terms cancel out, leaving $8\times7\times6\times5=1680$.