Name of distribution [closed]

Question

I am searching for the name of the following distribution on the set of positive integers (including zero).

Let $C\in \mathbb{Z}_+$ and $n\in \mathbb{N}$ are fixed.

Vector $p = (p_1,\ldots,p_n)$ is such that

1) $p_i\in \mathbb{Z}_+$. 2) $\sum_{i=1}^{n}p_i = C$.

The distribition of vectors $p$ is such that every vector is equal probable.

Anyone knows the name and where to read about it?

Answer 1

You can put the uniform distribution on any nonempty finite set whatsoever. In this case, you could call it the uniform distribution on the set of nonnegative integer solutions to an equation.