There are 12 points in a plane out of which 3 points are collinear. How many straight lines can be drawn by joining any two of them?

Step-by-step solution

The total number of ways to select 2 points out of 12 points is given by ¹²C₂ . ¹²C₂ = 12 11 2 1 = 66 . Since 3 points are collinear, joining any two of these 3 points results in the same line. The number of lines formed by these 3 points is ³C₂ = 3 2 2 1 = 3 . These 3 lines are counted as distinct lines in the total ¹²C₂ calculation, but they actually represent only 1 single line. Therefore, we must subtract the 3 lines and add back the 1 line that represents the collinear set. Total number of lines = ¹²C₂ - ³C₂ +