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 ?
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 .
divide(factorial(20), multiply(factorial(subtract(20, const_2)), factorial(const_2)))