select the correct answer.\nwhat is the number of possible permutations of 8 objects taken 4 at a time?\na…

Explanation:

Step1: Recall permutation formula

The formula for permutations is $P(n,r)=\frac{n!}{(n - r)!}$, where $n$ is the total number of objects and $r$ is the number of objects taken at a time. Here $n = 8$ and $r=4$.

Step2: Calculate factorial values

$n!=8! = 8\times7\times6\times5\times4\times3\times2\times1$, $(n - r)!=(8 - 4)!=4!=4\times3\times2\times1$. Then $P(8,4)=\frac{8!}{(8 - 4)!}=\frac{8\times7\times6\times5\times4!}{4!}$.

Step3: Simplify the expression

The $4!$ in the numerator and denominator cancels out. So $P(8,4)=8\times7\times6\times5=1680$.

Answer:

C. 1,680