Question

Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the points.

Answer 1

Total number of points = 18 

Out of 18 numbers, 5 are collinear and we get a straight line by joining any two points.

∴ Total number of straight line formed by joining 2 points out of 18 points = ¹⁸C₂ 

Number of straight lines formed by joining 2 points out of 5 points = ⁵C₂ 

But 5 points are collinear and we get only one line when they are joined pairwise. 

So, the required number of straight lines are

Hence, the total number of straight lines = 144