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?
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?