To count the number of distinct triangles:

Start with all possible triples of points.

From 12 points, the number of ways to choose any 3 is

$ \binom{12}{3}= \frac{12\cdot11\cdot10}{3\cdot2\cdot1}=220. $

Subtract the “invalid” triples that are collinear.

The only collinear sets of three points arise from the single line containing the 5 collinear points.

Number of ways to pick 3 points from those 5 is

$ \binom{5}{3}=10. $

Valid triangles = total triples − collinear triples.

$ 220-10 = 210. $

Hence, the total number of triangles that can be formed is 210.

Correct option: B