When you have combinations where numbers are $0,1,2,\dots,m$, meaning we have $n=m+1$ and $k$, is there a way to see how $k$ of them sum up to a given number?
For the sake of simplicity I have the numbers $0,1,2...,7$ (so $n=8$), and $k=3$. I need to find how much of these combinations with repetition sum up to $7$. By sum up, I mean the sum of all $3$ digits in each combination needs to be equal to $7$. Is there a formula for this?