MHT CET 2025 Mathematics question

There are 11 points in a plane of which 5 points are collinear. Then the total number of distinct quadrilaterals with vertices at these points is

(A)Correct
(B)
(C)
(D)

Answer: (A)

Solution

A quadrilateral needs 4 vertices, no three of which are collinear, so at most 2 of the chosen points may come from the 5 collinear points. Count by cases: choose 4 non-collinear points out of 6 non-collinear points: ; 1 from the 5 collinear and 3 from the 6 others:

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Question ID VK-102741