Consider a set of 12 points in a plane, out of which exactly 5 points are collinear and no other three points are collinear. The total number of distinct quadrilaterals that can be formed using these points as vertices is

Step-by-step solution

To form a quadrilateral, 4 points must be selected from the 12 points. The total number of ways to select 4 points is ¹²C₄ . ¹²C₄ = 12 11 10 9 4 3 2 1 = 495 A valid quadrilateral cannot be formed if all 4 points are collinear, or if 3 points are collinear and the 4^ th point is non-collinear. Case 1: All 4 points are chosen from the 5 collinear points. Number of ways = ⁵C₄ = 5 Case 2: 3 points are chosen from the 5 collinear points and 1 point is chosen from the remaining 7 non-collinear points. Number of ways = ⁵C