How do we calculate the maximum number of intersections possible for a given number of line segments?

Question

I heard that there is a formula to calculate the number of intersections possible as there is one for the circles...Plz. help//

Answer 1

If we have n line segments in general position (i.e. no two are parallel, no three are concurrent), then for each pair of lines there is exactly one intersection point, and vice versa.  Therefore, the number of intersection points is the same as the number of pairs of lines, which is given by:

n "choose" 2 = nC2 = [n * (n - 1)]/2

(Note: lines not in general position will have fewer intersection points.)

Answer 2

Simple formula for this is (to calculate max possible points of intersection with given number of lines) :

n * (n - 1) /2

Where n = number of lines

Enjoy!