Let $n\ge k\ge m\ge 0$ be integers. Consider the following formula:


Give two different proofs. On proof should use the factorial formula for $\binom{n}k$. The other proof should be combinatorial. Try to develop a question that both sides of the equation answer.

So this question asked us to prove the formula below in two ways, and while I got it for the 1st way [using the factorial formula for $\binom{n}k$], I still don't understand how I can prove this using a combinatorial proof. I'm having trouble constructing a counting argument. Can anyone help me out?


merged by quid Feb 28 at 23:50

This question was merged with Proving an identity with a combinatorial proof: $\binom{n}{k}\binom{k}{r}=\binom{n}{r}\binom{n-r}{k-r}$ because it is an exact duplicate of that question.