TS EAMCET · Maths · Permutation Combination
\(p\) points are chosen on each of the three coplanar lines. The maximum number of triangles formed with vertices at these points is
- A \(p^3+3 p^2\)
- B \(\frac{1}{2}\left(p^3+p\right)\)
- C \(\frac{p^2}{2}(5 p-3)\)
- D \(p^2(4 p-3)\)
Answer & Solution
Correct Answer
(D) \(p^2(4 p-3)\)
Step-by-step Solution
Detailed explanation
Total number of points in a plane is \(3 p\). \(\therefore\) Maximum number of triangles \(={ }^3{ }^p C_3-3 \cdot{ }^p C_3\) [Here, we subtract those triangles which points are in a line]…
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