Consider n people, each has k identical balls. Each people choose k different bins from m bins, constrained by the condition that there are no two people choose exactly the same k bins. For instance, there are 6 people A,B,C,D,E,F, each hold 2 balls and there are 4 different bins①，②，③，④. If A choose ①②, B choose ①③， C choose ①④, D choose ②③，E choose ②④，and F choose③④, then we call it a proper configuration since no two people choose exactly the same 2 bins
Now each people flip a unbiased coin, if HEAD appears then he put all his ball into the k bins he has chosen, each bin with one ball. He will do nothing if TAIL appears. Here comes the problem, given a proper configuration, everyone flip a coin and behave the way we described above. Can we infer the coin result of each people based on the number of balls in each bin?