Let's say there are $N$ objects ($n_0, n_1, n_2,...,n_{N-1}$), to be placed into $C$ containers ($c_0, c_1, c_2,...,c_{C-1}$), where $C >= N$, and $|c_j| = 1$. However, the method in which I do this will be a little different. I'm going to let each of the $N$ objects, $n_i$, choose $k$ random containers.
Supposing $N$ and $C$ are known, what is the minimum value of $k$ that could be chosen such that each $n_i$ can be placed into one of it's chosen $c_j$ with 'a reasonable probability'?
An example of this would be a teacher requesting available time slots ($k$) from his students ($N$). He would like to meet with each of them individually during one of the times he has available ($C$). How many time slots should he ask his students to provide?
There have been similar posts, but I couldn't find anything with these specifics. This one comes close: Distributing $k$ objects in $n$ containers - Probability distribution for Combinatorial problems
Any help would be appreciated.
