In a plane there are 37 straight lines of which 13 pass through point $A$ and 11 pass through the point $B$. Moreover, no three lines (apart from the lines passing through $A$ and $B$ ) pass through same point and no two are parallel. What is the number of points of intersection of the straight…

Question

In a plane there are 37 straight lines of which 13 pass through point $A$ and 11 pass through the point $B$. Moreover, no three lines (apart from the lines passing through $A$ and $B$ ) pass through same point and no two are parallel. What is the number of points of intersection of the straight lines?

Aicharya · Accepted Answer

Number of selection of two lines $={ }^{37} C_2$ Number of selection of two lines from lines which are concurrent at point $A={ }^{13} C_2$ Number of selection of two lines from lines which are concurrent at point $B={ }^{11} C_2$ $	herefore$ Total number of points of intersection $ ={ }^{37} C_2-{ }^{13} C_2-{ }^{11} C_2+2 $

In a plane there are 37 straight lines of which 13 pass through point $A$ and 11 pass through the point $B$.…

Solution