In a Plane there are 37 straight lines, of which 13 pass through the point A and 11 pass through the point B. Besides, no three lines pass through one point, no lines passes through both points A and B , and no two are parallel. Find the number of points of intersection of the straight lines.

The number of points of intersection of 37 lines is  $C237$. But 13 straight lines out of the given 37 straight lines pass through the same point A.

Therefore instead of getting  $C213$ points, we get only one point A. Similarly 11 straight lines out of the given 37 straight lines intersect at point B. Therefore instead of getting  $C211$ points, we get only one point B.

 Hence the number of intersection points of the lines is  $C237-C213-C211 +2$ = 535