# ball and bin problem with repeated tosses when bin is overflowed

There are m bins and n balls, each bin can hold k balls. The balls are randomly tossed into the bins. If one ball is tossed into a full bin, we say an overflow occurs and the ball will have another chance to randomly find a bin in m bins. Each ball has s chances to re-toss (include the first chance). question: how many balls are toss once, how many twice, ...? what is the distribution?

the problem is so hard!

thank you

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a lower bound or upper bound is also welcome! –  platinum Jan 20 at 15:28