I need some help in the following problem:
There are total $N$ balls where $n_1$ balls are of type 1, $n_1$ balls are of type 2 upto $n_p$ balls are of type $p$ i.e $n_1 + n_2 +...+n_p = N$.
Also, there are $M$ bins. A ball can be drawn independently out of $N$ balls and can be placed into any of the $M$ bins with uniform probability. Now, I have to find what is maximum number of distinct type of balls a bin can have with high probability. I am not sure how to solve this. Can this problem be mapped into any standard NP complete / approximation algo problem?