Question

What value is a permutation of n things taken r at a time divided by to get the combination of n things taken r at a time?

Answer 1

Answer:

A. r!

Step-by-step explanation:

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

Permutation of n things taken r at a time

$P_{(n,r)} = \frac{n!}{(n-r)!}$

Combination of n things taken r at a time:

$C_{n,r} = \frac{n!}{r!(n-r)!}$

Division:

$\frac{P_{(n,r)}}{C_{n,r}} = \frac{\frac{n!}{(n-r)!}}{\frac{n!}{r!(n-r)!}} = \frac{n!}{(n-r)!} \times \frac{r!(n-r)!}{n!} = r!$

So the correct answer is:

A. r!