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?

  • 2
    $\begingroup$ Yes, it’s correct. $\endgroup$ – Brian M. Scott Nov 13 '16 at 17:53
  • $\begingroup$ @BrianM.Scott Thank you :) At least one positive information for me today $\endgroup$ – Johny Nov 13 '16 at 18:44
  • $\begingroup$ And it’s a comment that I like to make! :-) $\endgroup$ – Brian M. Scott Nov 13 '16 at 18:47

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