Question:
If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?
Solution:
Let the number of intersection point of first line =0
Let the number of intersection point of 2nd line = 1
Let the number of intersection point of 3rd line = 2+1
Let the number of intersection point of 4th line = 3+2+1
. . .
Let the number of intersection point of nth line =(n-1) +(n-2)…..(3)(2)(1), where n=20
S = ( n – 1) × n/2
=19×10
=190