Question

select the correct answer. what is the number of possible permutations of 8 objects taken 4 at a time? a. 24 b. 70 c. 1,680 d. 40,320

Explanation:

Step1: Recall permutation formula

The formula for permutations of $n$ objects taken $k$ at a time is $P(n,k)=\frac{n!}{(n-k)!}$

Step2: Substitute $n=8$, $k=4$

$P(8,4)=\frac{8!}{(8-4)!}=\frac{8!}{4!}$

Step3: Expand factorials and simplify

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

Step4: Calculate the product

$8\times7=56$, $56\times6=336$, $336\times5=1680$

Answer:

C. 1,680