Probability That 1 Was Selected Given Increasing Order
You draw $r$ integers one at a time, without replacement, uniformly at random from $\{1, 2, \dots, n\}$. Someone tells you that the numbers came out in increasing order. Given that information, what is the probability that
$ was among the numbers selected?
Derive a general formula in terms of $r$ and $n$, then compute the answer for $r = 5$ and $n = 100$.
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