Question

in a plane there are 27 straight lines,of which 13 passes through the point A and 11 passes through the point B.Besides no three lines passes through one point.No lines passes through both points A and B and no two are parallel.Find the numbers of point of intersections of the straight lines?

Answer 1

Interesting question. Thanks for asking it.
This question is from Permutations and combinations chapter.

The number of points of intersection of 37 lines will be equal to ³⁷C₂
13 straight lines out of 37 passes through A .
Instead of getting ¹³C₂ points, we get only one point A
11 straight lines out of 37 passes through point B. Instead of getting ¹¹C₂  points, we get only one point B.
Hence number of intersection points of lines
³⁷C₂-¹³C₂ -¹¹C₂+2=535

Answer 2

Answer:

Step-by-step explanation: