Matematické Fórum

Skrytý text:

Let's separate 2k - element set C into two k-element sets A,B. Every k element subset of C "induces" i-element subset of A and k-i - element subset of B (for some i from {0,..,k}). Also, every i-element subset of A and k-i - element subset of B "induces" k - element subset of C so there is a bijection between k-element subsets of C and the set of pairs (i-element subset of A, k-i element subset of B) for i from {0,..k}. The number of elements of the first set is

and the number of elements of the second set is
.
So the equality of these numbers follows from the mentioned bijection.