Question

How many triangles can be formed by joining 12 points 7 of which are collinear?

Answer 1

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.

Answer 2

Answer:

210

Step-by-step explanation:

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.