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  4. If there are nine straight lines of which five are concurrent at a point and the other four are concurrent at another point and no two of these nine lines are parallel, then the number of points of intersection is equal to

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Q. If there are nine straight lines of which five are concurrent at a point and the other four are concurrent at another point and no two of these nine lines are parallel, then the number of points of intersection is equal to

NTA AbhyasNTA Abhyas 2020Permutations and Combinations

Solution:

Nine straight lines will intersect at ${ }^{9} C_{2}$ points Five are concurrent at one point so there will be loss of ${ }^{5} C_{2}$ points
Four other are concurrent at another point, so there is further loss of ${ }^{4} C_{2}$ points.

But we will have these two points at which the lines are concurrect.
So, total number of points $={ }^{9} C_{2}-{ }^{5} C_{2}-{ }^{4} C_{2}+2=36-10-6+2=22$