If there are six straight lines in a plane, no two of which are parallel and no three of which pass through the same point, then find the number of points in which these lines intersect.

Answer

15

Explanation

There are six straight lines `L_(1),L_(2),L_(3),L_(4),L_(5),L_(6)` in a plane.
Since no two lines are parallel and no three of which pass through the same point, we have maximum points of intersection.
Line `L_(1)` intersect five lines, so there will be five points of intersection.
Similarly, for each of the lines `L_(2),L_(3),L_(4),L_(5),L_(6)`, there will be five points of intersection.
But there will be double counting .
So, total number of points of intersection is `(5xx6)/(2)=15`