I'm trying to prove that the number of solutions of
$ x_1 + x_2 + ... + x_g \le n$
is
$ \dbinom{g + n}{n} $
so far I've been able to show that the number of solutions of
$ x_1 + x_2 + ... + x_g = n$
is
$ \dbinom{g + n - 1}{n} $
But I can't manage to see how to get from my result to the goal result. I used a partitioning argument for my result. Is this the wrong way of going about it?
Thanks!