Question

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 line passes through both points A and B no two lines are parallel. Find the number of points of intersection of the straight lines.

Answer 1

The number of points of intersection of 37 straight lines is ${37}_{C_2}$.

But 13 straight lines out of the given 37 straight lines pass through the same point A.

Therefore, instead of getting ${13}_{C_2}$ points, we get only one point A. Similaly, 11 straight lines out of the given 37 straight lines intersect at point B. Therefore, instead of getting ${11}_{C_2}$ points, we get only one point B.

Hence, the number of intersection points of the line is

${37}_{C_2}-{13}_{C_2}-{11}_{C_2}+2=666-78-55+2=535$