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, no two are parallel. Then the number of intersection points the lines have is equal to _____.
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, no two are parallel. Then the number of intersection points the lines have is equal to _____.
The correct option is A 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.
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 is 37C2 - 13C2 - 11C2 +2 = 535 (We added 2 because points A and B are also included).
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.
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 is 37C2 - 13C2 - 11C2 +2 = 535 (We added 2 because points A and B are also included).
