AP EAMCET · Maths · Permutation Combination
Suppose \(t_n\) is the number of triangles formed using the vertices of a regular polygon of \(n\) sides. If \(t_{n+1}=t_n+28\), then \(n=\)
- A 11
- B 9
- C 8
- D 7
Answer & Solution
Correct Answer
(C) 8
Step-by-step Solution
Detailed explanation
\(t_n = \binom{n}{3}\) \(\binom{n+1}{3} = \binom{n}{3} + 28\) \(\binom{n+1}{3} - \binom{n}{3} = 28\) \(\binom{n}{2} = 28\) (Using Pascal's identity \(\binom{k}{r} = \binom{k-1}{r} + \binom{k-1}{r-1}\), so \(\binom{n+1}{3} - \binom{n}{3} = \binom{n}{2}\))…
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