NDA 2 2025 Maths, question 36

Topic: Algebra

Passage · Q35 to Q36

There are $8$ points on a plane out of which $4$ points are collinear.

Q36

How many quadrilaterals can be formed by joining these points?

(a) $70$
(b) $69$
(c) $53$ Correct answer
(d) None of the above

Solution.

Answer: (c) $53$

Any 4 of the 8 points: $\binom{8}{4} = 70$ .
Remove sets with 3 collinear points and 1 other: $\binom{4}{3} \times 4 = 16$ .
Remove the set of all 4 collinear points: 1. So $70 - 16 - 1 = 53$ .

Trap: This assumes no other three points are collinear, as in question 35.