For the following two (02) items: There are 8 points on a plane out of which 4 points are collinear. How many triangles can be formed by joining these points?

Step-by-step solution

Total number of points on the plane is n = 8 . Number of collinear points is m = 4 . The total number of triangles that can be formed by joining n points out of which m are collinear is given by ^ n C₃ - ^ m C₃ . Substituting the values, we get ⁸C₃ - ⁴C₃ . ⁸C₃ = 8 7 6 3 2 1 = 56 ⁴C₃ = 4 3 2 3 2 1 = 4 Total number of triangles = 56 - 4 = 52 . Answer: 52