# Thread: Counting number of solutions for an inequality

1. ## Counting number of solutions for an inequality

2. $\sum\limits_{j = 0}^n {{j+k-1}\choose j}$

3. Originally Posted by qtpipi

Notice that if $x_1 + \dots + x_k \leq n$
where $0 \leq x_i$ for all i, then
$x_1 + \dots +x_k + x_{k+1} = n$
where $0 \leq x_i$ for all i.