# Combinatorial intuition of identity

Is there any combinatorial intuition to prove this identity $r\cdot \binom{n}{r}=n\cdot\binom{n-1}{r-1}$?

Hint: Consider forming a committee from a group of $n$ people where one member of the committee is special, e.g. the chairman of the committee. Try counting this in two different ways.
• @pyschedelicsid yes. The same logic will show the more general identity $\binom{n}{r}\binom{r}{k}=\binom{n}{k}\binom{n-k}{r-k}$, your specific case is where $k=1$ – JMoravitz Sep 26 '17 at 17:39