Out of 8 given points, 3 are collinear. How many different straight lines can be drawn by joining any two points from those 8 points?

Step-by-step solution

The total number of ways to select 2 points out of 8 points is given by ⁸C₂ . ⁸C₂ = 8 7 2 1 = 28 . 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 in the total ⁸C₂ calculation, but they actually represent only 1 unique line. Therefore, we must subtract the 3 lines and add back the 1 unique line. Total number of lines = ⁸C₂ - ³C₂ + 1 = 28 - 3 + 1 = 26 . Answer: 26