Find the number of triangles whose sides are formed by the sides and the diagonals of a regular heptagon. (The vertices of triangles need not be the vertices of the heptagon).
First of all, there are $7 \cdot 4 / 2 = 14$ diagonals and $7$ sides. Then I tried drawing this out — except that regular heptagons are hard to draw and there are a lot of lines. I thought you could choose 3 lines to be sides of triangles but that won't always work because sometimes they just don't form a triangle. How can I approach / solve this problem>