NDA 2024 · PYQ · Permutations and Combinations · easy
A triangle PQR is such that 3 points lie on the side PQ, 4 points on QR and 5 points on RP respectively. Triangles are constructed using these points as vertices. What is the number of triangles so formed?
A.205✓ Correct
B.206
C.215
D.220
Explanation
Total points = 12. Total ways to choose 3 points = C(12,3) = 220. Subtract collinear triples: C(3,3) + C(4,3) + C(5,3) = 1 + 4 + 10 = 15. Number of triangles = 220 − 15 = 205.
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