Editing Bijective proof (section)

==Basic examples==

=== Proving the symmetry of the binomial coefficients ===

The symmetry of the binomial coefficients states that

:<math> {n \choose k} = {n \choose n-k}. </math>

This means that there are exactly as many [[combination]]s of {{math|''k''}} things in a set of size {{math|''n''}} as there are combinations of {{math|''n''&nbsp;&minus;&nbsp;''k''}} things in a set of size&nbsp;{{math|''n''}}.

The key idea of the bijective proof may be understood from a simple example: selecting {{math|''k''}} children to be rewarded with ice cream cones, out of a group of {{math|''n''}} children, has exactly the same effect as choosing instead the {{math|''n''&nbsp;&minus;&nbsp;''k''}} children to be denied ice cream cones.