slove the problem in c++ with details explantaion

Question

Prove of a recursive definition (Combination of r items from n items)

Answer 1

(N choose r) = N! / [ r ! (n - r) ! ]

N for the 1st choice

N-1 for the 2nd choice

N-2 for the 3rd choice

....

N-r+1 for the Rth choice

N(N-1)(N-2)....(N-r+1) =

N(N-1)(N-2)...(N-r+1)(N-r)(N-r-1)...*3*2*1 / (N-r)! <--- multiplies top and bottom by (n-r)!

since there are r items, there are r! ways to arrange and their order does not matter.

So we can remove them by dividing by r! in the denominator.

Therefore (N choose r) = N! / [ r ! (N-r)! ]