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Previous Year Question (PYQs)
3
Out of $(2n+1)$ consecutively numbered tickets, three tickets are drawn at random. The probability that the numbers on them are in arithmetic progression is
Solution
Total ways: $\binom{2n+1}{3}$
AP triples: choose middle term and common difference
Total AP = $n(2n+1)$
Probability = $\frac{n(2n+1)}{\binom{2n+1}{3}} = \frac{3n}{4n^2 -1}$
Final Answer: $\boxed{\frac{3n}{4n^2 -1}}$
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