Starting from $\langle 0,0\rangle$ and going to $\langle n,m\rangle$ where $n,m$ are nonnegative integers, and under the condition that by each step one of the coordinates increases with $1$ you must make $n+m$ steps in total. Exactly $n$ steps must be elected to be one of the steps where the first coordinate grows.
There are:$$\binom{n+m}n$$ possible selections.