Question

fill in the blank so that the resulting statement is true. the number of possible permutations if r objects are taken from n items is ( _np_r = ) ______. the number of possible permutations if r objects are taken from n items is ( _np_r = ) dropdown options: ( \frac{n!}{(n - r)!} ), ( \frac{r!}{(r - n)!} ), ( \frac{r!}{(n - r)!} ), ( \frac{n!}{(r - n)!} ))

Explanation:

Step1: Recall permutation formula

Permutations of r items from n: order matters. The formula is $\frac{n!}{(n-r)!}$.

Step2: Match with options

Check the dropdown options. The first option is $\frac{n!}{(n-r)!}$, which is correct.

Answer:

$\frac{n!}{(n-r)!}$