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, and no two are parallel. Then the number of intersection points the lines have is equal to

(A)  535

(B)  601

(C)  728 

(D)  None of these

Answer 1

Correct option (A) 535 

In the general position, 37 straight lines have ³⁷C₂ points of intersection. But 13 straight lines passing through the point A yield one intersection point instead of ¹³C₂ and 11 straight lines passing through the point B yield one intersection point instead of ¹¹C₂ .

Therefore, the lines have ³⁷C₂ - ¹³C₂ - ¹C₂  + 2 points of intersection. This gives

666 – 78 – 55 + 2 = 535