Hello candidate,

In the Question it's mentioned that no more than 4 points can lie on the circle of the circle cannot pass through more than a set of four points.

So, it's obvious that from the parallel lines only one point can be included. Hence, here are the following combinations which can be found-

Case I: 4C1* 5C1*6C2

Case II: 4C1* 5C2*6C1

Case III: 5C2* 6C2

Case IV: 5C3* 6C1

Case V: 6C3* 5C1

Hope that This answer was helpful!!