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}=(n!)/((n-r)!))\\\\_(r)^(n)\textrm{C}=(n!)/(r!*(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}`