Question
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?
NDA
Mathematics
Permutation Combination
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. 70
- B. 69
- C. 53
- D. None of the above
Answer
C. 53
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 ^ 8 C_ 4 = 70. A quadrilateral cannot be formed if 3 or 4 selected points are collinear. Number of ways to select 4 collinear points is ^ 4 C_ 4 = 1. Number of ways to select 3 collinear points and 1 non-collinear point is ^ 4 C_ 3 ^ 4 C_ 1 = 4 4 = 16. Total number of quadrilaterals that can be formed is 70 - (1 + 16) = 53. Answer: 53
Related: Mathematics — Permutation Combination · All PYQ Banks