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

Step-by-step solution

Total number of points is 8 . Number of collinear points is 4 . Total number of ways to select 4 points from 8 points is ⁸C₄ = 70 . A quadrilateral cannot be formed if 3 or 4 selected points are collinear. Number of ways to select 4 collinear points is ⁴C₄ = 1 . Number of ways to select 3 collinear points and 1 non-collinear point is ⁴C₃ ⁴C₁ = 4 4 = 16 . Total number of quadrilaterals that can be formed is 70 - (1 + 16) = 53 . Answer: 53