How would you show that $$\binom{n}{k}\binom{k}{m}\binom{m}{r} = \binom{n}{r}\binom{n-r}{n-m}\binom{n-m}{k-m}$$ for $n\geq k\geq m\geq r$ ?
Proving that $\binom{n}{k}\binom{\smash{k}}{m}\binom{m}{r} = \binom{n}{r}\binom{n-r}{n-m}\binom{n-m}{n-k}$
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combinatorics
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0Use the definition of the Binomial coefficient. – 2016-02-09