Number of triangles in all subgraphs of a complete graph.

Question

So I know that for say $V = \{1, 2, ..., n\}$ that there are $2^{n\choose2}$ simple graphs with vertex set $V$ and that there are ${n\choose3}$ triangles in a given graph, but how would I proceed to find the total number of triangles in all those graphs?

Answer 1

Hint: Consider how many subgraphs include a given triangle.