Hi there,

Apparently it should be rather easy, but I cannot figure it out. We have n piles and want to divide at most k over these piles. The number of possibilities is (n+k) choose n, but why?

Example to illustrate the problem:

n = 2

k = 2

The possibilities: (0,0), (0,1), (1,0), (2,0), (1,1), (0,2)

## Binomial question

### Re: Binomial question

It is appropriate to use a Stars and Bars argument in this case: http://en.wikipedia.org/wiki/Stars_and_ ... atorics%29 . You can add an extra pile to make the problem easier where the extra pile is the remaining number of objects that you don't use. Hence. you want to distribute k objects over n+1 piles, and the argument follows:)