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

NPr  = n! / (n-r)!

nCr = n! / r! (n-r)!

nPr / nCr  = n! (n-r)!  * r!(n-r)! / n!  = r!


The answer is r factorial (r!)

Answer 2

Answer with explanation:

$_{r}^{n}\textrm{P}$ = Permutation of n things taken r at a time

$_{r}^{n}\textrm{C}$=Combination of n things taken r at a time

$_{r}^{n}\textrm{P}=\frac{n!}{(n-r)!)}\\\\_{r}^{n}\textrm{C}=\frac{n!}{r!\times(n-r)!)}$

$_{r}^{n}\textrm{C}$ contains one term r!, in the denominator which is not in $_{r}^{n}\textrm{P}$.

When we divide $_{r}^{n}\textrm{P}$ by r! that is $\frac{_{r}^{n}\textrm{P}}{r!}=_{r}^{n}\textrm{C}$