The maximum number of points of intersection occurs when no three of the crossing lines are coincident.
In that case, each point of intersection is associated with 2 crossing lines, and hence with 2 points on L_{1}
and 2 points on L_{2}.
So the number of intersection points is equal to the number of ways of choosing 2 points on L_{1}
multiplied by the number of ways of choosing 2 points on L_{2}.

The number of ways of choosing 2 points from 100 is just the binomial coefficient
(100

2) = 100 * 99 / 2 = 4,950.
The maximum number of intersection points is therefore 4,950 * 4,950 = 24,502,500.