**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