Consider a 4 × 5 rectangular grid of dots. If you pick three dots, they might or might not form a triangle. If you pick three more, those might or might not form a triangle as well. And if you happen to find two sets of three dots each of which form triangles, the intersection of those triangles might or might not form a quadrilateral. How many pairs of triangles (all vertices of which are dots in a given 4 × 5 grid) have a quadrilateral intersection?

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