SOLUTION: how many triangles can be obtained by joining 12 points, five of which are collinear ?

Question 834980: how many triangles can be obtained by joining 12 points, five of which are collinear ?
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!

[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

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