TS EAMCET · Maths · Permutation Combination
If \(t_n\) denotes the number of triangles formed with \(n\) points in a plane, no three of which are collinear and if \(t_{n+1}-t_n=36\), then \(n\) is equal to
- A \(7\)
- B \(8\)
- C \(9\)
- D \(10\)
Answer & Solution
Correct Answer
(C) \(9\)
Step-by-step Solution
Detailed explanation
\(t_n=\) The number of triangles formed with \(n\) points in a plane, no three of which are collinear. i.e., \[ \begin{aligned} & t_n={ }^n C_3 \\ & t_{n+1}={ }^{n+1} C_3 \end{aligned} \] \[ \Rightarrow \quad t_{n+1}={ }^{n+1} C_3 \] Now, \(t_{n+1}-t_n=36\)…
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