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

Instead of getting ¹³C₂ points of intersection, we get only one point A. 11 lines passes through same point 13.

Instead of getting ¹¹C₂ point of intersection, we get only one point B.

Total no. of point of intersection

= ³⁷C₂ – $\left( 13C_{2} - 1 \right) - \left( 11C_{2} - 1 \right)$

= 666 – 77 – 54 = 535