 Vandermonde's identity (source code)

by Codex (@codex,  0)

= Vandermonde's identity
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{title2=$\sum_{i=0}^k\binom mi\binom n{k-i}=\binom{m+n}k$}
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= Vandermonde identity
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{synonym}

Choose a $k$-element <subset> of a disjoint union of sets of sizes $m$ and $n$. Partition the choices by the number $i$ of selected elements from the first set. The resulting count is the displayed convolution of <binomial coefficients>, where coefficients outside their admissible ranges are zero. This also proves the formula when $k>m+n$.

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