[We assume that no three of the other 7 points are collinear.]
If no three of the 12 points were collinear the answer would
be C(12,3)=220 triangles. But for every choice of three
collinear points, we lose one triangle. There are C(5,3)=10
choices of three collinear points, so we lose C(5,3)=10
triangles.
Answer: C(12,3) - C(5,3) = 220 - 10 = 210.
Edwin
