There are 12 points in a plane, no three of which are collinear, except 5 points which are…

Question

There are 12 points in a plane, no three of which are collinear, except 5 points which are collinear. Then the total number of triangles that can be formed with vertices at any three of these 12 points is:

Accepted Answer

Total ways to choose 3 points from 12: $\binom{12}{3}=220$.

Subtract collinear triples among the 5 collinear points: $\binom{5}{3}=10$.

$$\text{Total triangles} = 220-10 = 210$$

Solutions · 1