If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?
Select.
A) 110
B) 130
C) 150
D) 170
E) 190

Rationale: if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 20 lines is 20 c 2 = 190 the answer is e .
Answer: E