How many monotically functions $f: \{1,2, ..., m\} \rightarrow \{1,2, ..., n\}$ are there if $f(k) = l$, where $1 \le k \le m$ and $1 \le l \le n$?
I tried to compute as answer in counting monotonically increasing functions and I has this result: ${{(k-1)+(l-1)} \choose {l-1}} \cdot { {(m-k)+(n-l)} \choose {n-l}}$. Is this correct?