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Let $A=\{i: 1 \leq i \leq n\} \subset \mathbb{N} $ and $B \subset A$, $|B|=k$ ($k < n$). What's the probability that $\gcd(B)>1$?

EDIT: $n$ and $k$ are given. I think this can be solved with inclusion-exclusion principle?

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    Perhaps it may be useful to know that the probability that a number $k < n$ selected being coprime to $n$ is $\phi(n)/n$.2012-08-05

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