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them with other sets that are easier to count. Additionally, the nature of the bijection itself often provides powerful insights into each or both of the sets.

Basic examples

Proving the symmetry of the binomial coefficients

The symmetry of the binomial coefficients states that

:

This means that there are exactly as many combinations of things in a set of size as there are combinations of things in a set of size .

The key idea of the bijective proof

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