Monday, 19 March 2018

combinatorics - Combinatorial interpretation for the identity sumlimitsibinommibinomnji=binomm+nj?

A known identity of binomial coefficients is that
\sum_i\binom{m}{i}\binom{n}{j-i}=\binom{m+n}{j}.
Is there a combinatorial proof/explanation of why it holds? Thanks.

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