Answer:

10 points lie in a plane, of which 4 points are collinear. Barring these 4 points, no 3 of the 10 points are collinear. How many distinct quadrilaterals can be drawn?

I have solved it in the following manner:

Considering the first case; 1 point from the line and rest 3 out of 6, which are not collinear I get: 4C1⋅6C3=80

second case: 2 points from the collinear ones and rest from the 6 I get: 4C2⋅6C2=90

third case: using four points from the six non-collinear ones, I get: 6C4=15

Adding them up I got 185 ways, but the answer is 209.