Help: Graph Theory Formula for Gzn Edges w/z & n

[TinyTex]

z = positive int, Y = {1 2 3 ... n} where Y = n greater or equal to z
defines G^z_n

1)work out a formula in n and z for the edges in G ^z_n, the vertex set to include all possible z elements subsets of Y

help please what's the formula?
i know how to work out the number of vertices in a formula
which is n!/z!(n-z)!
been stuck on the formula for the edges for ages... i also know how to calculate the edges if its a complete graph e.g. G¹_n is n(n-1)/2 since degree (v)= doubles the edges

e.g. G²₃ has 3 vertexs of {12}{13}{23} no edges

 

[Jhero]

The formula for the number of edges in Gzn is n!/[z!(n-z)!]*(z*(z-1))/2. This formula is derived from the number of combinations of z elements subsets of Y and the fact that each of these combinations has z(z-1)/2 edges between them.