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Previous Year Question (PYQs)



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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