select the correct answer. what is the number of possible permutations of 8 objects taken 4 at a time? a. 24…

Explanation:

Step1: Recall permutation formula

The formula for permutations of $n$ objects taken $r$ at a time is $P(n,r)=\frac{n!}{(n - r)!}$. 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 $P(8,4)=\frac{8!}{4!}=\frac{8\times7\times6\times5\times4!}{4!}$.

Step3: Simplify the expression

Cancel out the $4!$ terms. We get $P(8,4)=8\times7\times6\times5 = 1680$.

Answer:

C. 1,680