Question
For the following two (02) items: There are 8 points on a plane out of which 4 points are collinear. How many triangles can be formed by joining these points?
NDA
Mathematics
Permutation Combination
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. 56
- B. 54
- C. 53
- D. 52
Answer
D. 52
Step-by-step solution
Total number of points on the plane is n = 8. Number of collinear points is m = 4. The total number of triangles that can be formed by joining n points out of which m are collinear is given by ^ n C_ 3 - ^ m C_ 3 . Substituting the values, we get ^ 8 C_ 3 - ^ 4 C_ 3 . ^ 8 C_ 3 = 8 7 6 3 2 1 = 56 ^ 4 C_ 3 = 4 3 2 3 2 1 = 4 Total number of triangles = 56 - 4 = 52. Answer: 52
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