In a plane there are 37 st. 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

Question

In a plane there are 37 st. 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

Tardigrade Admin · Accepted Answer

The number of points of intersection of

37

st. lines

=^{37} C_{2}

.
But

13

of them pass thro’ the point

A

.

∴

instead of getting

^{37} C_{2}

points, we get merely one point. Similarly

11

st. lines out of the given

37

st. lines intersect at

B

.

∴

instead of getting

^{37} C_{2}

points, we get only one point. Hence the number of points of intersection the lines is

^{37} C_{2} -^{13} C_{2} -^{11} C_{2} + 2

= 535

$535$

$601$

$728$

none of these

Q. In a plane there are 37 st. 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

535

601

728

none of these

$535$

$601$

$728$