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Question

In a plane there are 37 straight lines of which 13 pass through point A and 11 pass through the point B. Besides, no three lines pass through one point, no line passes through both A and B, and no two lines are parallel.    
Then the total number of intersection points of the lines are 
  1. 601
  2. 728
  3. 535
  4. 426


Solution

The correct option is C 535

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. 
Similary, 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 is
= 37C2 13C2 11C2+2 
=535

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