There are 10 points in a plane out of which 4 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 10 points is given by ¹⁰C₂ . ¹⁰C₂ = 10 9 2 1 = 45 . Since 4 points are collinear, joining any two of these 4 points results in the same line. The number of ways to select 2 points from these 4 is ⁴C₂ . ⁴C₂ = 4 3 2 1 = 6 . These 6 lines are counted as distinct lines in the total of 45, but they actually represent only 1 unique line. Therefore, we subtract the 6 lines and add back the 1 line that they form. Total number of lines = 45 - 6 + 1 = 40 . Answer: 40