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May 16th, 2017, 11:53 AM   #1
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System of distinct representatives

> Determine for which $k,n\in \mathbb N, 1\le k \le n$ the system $\{1,2,...,n\}\choose k$ has a system of distinct representatives.

Well I think the solution is $k=n,k=1,k=n-1$. But I don't know how to prove it. I should verify the Hall condition somehow, but how? Any help would be appreciated.
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