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I was thinking about the fact that $\frac{1}{\zeta(n)}$ is the probability that $n$ randomly chosen integers are coprime, and wondered if there were “natural” ways in which $e^{-n}$ (for $n>0$) and $\frac{1}{\Gamma(n)} $(provided that $0 < \frac{1}{\Gamma(n)} < 1$) might be interpreted as probabilities with respect to a property of some structure on $n$ objects?

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    If $n$ is a positive non-zero integer, $\Gamma(n)=(n-1)!$. I guess you can think of some probabilistic interpretation for that.2011-03-01

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