Is there a strategy of placing $m$ balls into $n$ bins of varying capacities so that no allocation is more probable than any other? For example, suppose we have two balls to be placed in two bins, each big enough to hold the two balls. There are three possibilities: one ball in each bin, and both balls in either one of the bins. What sampling procedure will generate any of these possibilities equally?
Equiprobable allocation of balls into bins
combinatoricsprobabilitysampling
Best Answer
To decide the number of balls $a_1$ in the first bin, count the number of possible arrangements in the other $n-1$ bins if $a_1=0$, or $a_1=1$, and so on. Then pick a random number with proportional probabilities,to decide the value of $a_1$. Then go onto the next bin.