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