Answer:
A. r!
Step-by-step explanation:
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
Permutation of n things taken r at a time
[tex]P_{(n,r)} = \frac{n!}{(n-r)!}[/tex]
Combination of n things taken r at a time:
[tex]C_{n,r} = \frac{n!}{r!(n-r)!}[/tex]
Division:
[tex]\frac{P_{(n,r)}}{C_{n,r}} = \frac{\frac{n!}{(n-r)!}}{\frac{n!}{r!(n-r)!}} = \frac{n!}{(n-r)!} \times \frac{r!(n-r)!}{n!} = r![/tex]
So the correct answer is:
A. r!
