I have, say, 24 objects spread across 10 boxes. Each object can independently fall into any box (equal probability to any box).
Stars and bars let's me estimate number of possible combinations. But what's the probability distribution of number of objects in the fullest box?
Or to be more concrete, what's the possibility that at least one box will contain at least 6 objects? Or exactly one with exactly 6 objects?
I suspect that I could replace !******! with an apple to estimate the probability of at least one box with exactly 6 objects but what about the former questions? Are these solvable by stars'n bars?