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

Answer: (A)

535

Answer 2

The number of points of intersection of 37 straight lines is ³⁷C₂. But 13 of them pass through the point A. Therefore instead of getting ¹³C₂ points we get merely one point. Similarly 11 straight lines out of the given 37 straight lines intersect at B. Therefore instead of getting ¹¹C₂ points, we get only one point. Hence, the number of intersection points of the lines is³⁷C₂ – ¹³C₂ – ¹¹C₂ + 2 = 535.