If 23 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?
Choices:
A) 176
B) 253
C) 342
D) 458
E) 560

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 23 lines is 23 c 2 = 253 the answer is b ."
Answer: B