Question

Find the maximum number of points of
intersection of 7 straight lines and 5 circles when 3 straight
lines are parallel and 2 circles are concentric.​

Answer 1

There are exactly 3 types of intersection points:

Between a line and a line (6C2⋅1=15).

Between a line and a circle (6C1⋅5C1⋅2=60).

Between a circle and a circle. This is the case that you were forgetting. There are 5 circles in total, so there are 5C2 ways to choose the two circles that will intersect. These two circles can intersect at most 2 times. This yields 5C2⋅2=20.

Summing everything together, we obtain 15+60+20=95.