In a plane there are 37 straight lines, of which 13 passes through the point A and 11 passes through point B. Besides, no three lines passes through one point no line passes through both points A and B and no two are parallel, then find the number of points of intersection of the straight line.

Options

A. 533
B. 535
C. `""^(37)C_(2)-""^(24)C_(2)`
D. none of these

Explanation

The number of point of intersection of 37 straight lines is `""^(37)C_(2)`. But 13 straight lines out of the given 37 straight lines pass through the same point A. Therefore, instead of getting `""^(13)C_(2)` points, we get merely one point A. Similarly, 11 straight lines out of the given 37 straight lines intersect at point B. Therefore, instead of getting `""^(11)C_(2)` points, we get only one point B.
Hence, the number of intersection points of the lines is
`""^(37)C_(2)-""^(13)C_(2)-""^(11) C_(2)+2=535`.