JEE Mains · Maths · STD 11 - 6. permutation and combination
Let \(P_{1}, P_{2}, \ldots \ldots, P_{15}\) be \(15\) points on a circle. The number of distinct triangles formed by points \(P_{i}, P_{j}, P_{k}\) such that \(i+j+k \neq 15\), is :
- A \(12\)
- B \(419\)
- C \(443\)
- D \(455\)
Answer & Solution
Correct Answer
(C) \(443\)
Step-by-step Solution
Detailed explanation
Total Number of Triangles \(={ }^{15} \mathrm{C}_{3}\) \(\mathrm{i}+\mathrm{j}+\mathrm{k}=15 \text { (Given) }\) \([Image]\) Number of Possible triangles using the vertices \(\mathrm{P}_{\mathrm{i}}, \mathrm{P}_{\mathrm{j}}\) \(P_{k}\) such that \(i+j+k \neq 15\) is equal to…
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