Q. 265.0( 1 Vote )

There are 18 points in a plane of which 5 are collinear. How many straight lines can be formed by joining them?

Answer :

A line is formed by joining two points.


If the total number of points is 18, the total number of lines would be = 18C2


But 5 points are collinear, so the lines made by these points are the same and would be only 1.


Hence there is 1 common line joining the 5 collinear points.


As these 5 points are also included in 18 points so these must be subtracted from the total case , i.e. 5C2 must be subtracted from 18C2 .


Finally, the number of straight line = 18C2 - 5C2 + 1


= 144 lines


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