Number of Integer solutions for this optimization problem

Question

What is the number of integer solutions to the problem $$\sum_{i=1}^{i=k}x_i = n$$ subject to $\forall_i\ \ x_i \ge 0 $

note This should hold for both cases $k < n$ and $k \ge n$

Is order of the $x_i$'s important? – Dan Sep 14 '14 at 11:25 — Dan, Sep 14 '14 at 11:25

score 1 · Accepted Answer · answered Sep 14 '14 at 11:25

1

This is given by the formula $$CC_k^n = {n+k-1 \choose n}$$

answered Sep 14 '14 at 11:25

Snufsan

so is this problem equivalent to distributing $n$ distinct balls into $k$ distinct boxes? – bistaumanga Sep 14 '14 at 11:58
$n$ similar balls into $k$ distinct boxes – Snufsan Sep 14 '14 at 12:03

1 Answers1