double counting
Counting one set of objects two different, valid ways, proving the two resulting expressions equal.
A double-counting proof fixes a single set and computes its size two different ways; since both expressions count the same objects, they must be equal.
Examples
Counting k-subsets directly gives \binom{n}{k}; counting by which n-k elements are excluded gives \binom{n}{n-k}.
See also
Point table
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