Suppose I have the equation $x_1 + x_2 + ... + x_r = n$, for each $x_i \in \mathbb{N}$ and $n \in \mathbb{N}$ ($\mathbb{N}$ does not contain $0$).
We know that the number of solutions to this equation is ${n-1\choose r-1}$. But what if we wanted to find the number of UNIQUE solutions to the given equation? ${n-1\choose r-1}$ overcounts the solutions $(y_1, y_2, ..., y_r)$ with all of it's permutations $(y_1', y_2', ..., y_r')$?