- #1

- 986

- 9

## Homework Statement

Count the solutions in nonnegative integers x

_{1},...,x

_{k}to x

_{1}+ ... + x

_{k}=n

## Homework Equations

There's a Theorem in the chapter (shows that the answer is "n+k-1 choose k-1" but we're not allowed to use it.

## The Attempt at a Solution

Well, obviously you can just have x

_{1}and make equal to n, or you can make x

_{1},...,x

_{k=n }all equal to one, or do a bunch of stuff in between.

No stunning revelations for me, though. Ideas for how to construct a formula?