= Uniform balls-in-bins allocation
{title2=$(B_1,\ldots,B_m)\sim\operatorname{Multinomial}(n;1/m,\ldots,1/m)$}
Place $n$ labelled balls independently into $m$ labelled bins, each with probability $1/m$. The vector of bin counts has a <multinomial distribution>, and each count separately has the <binomial distribution> $\operatorname{Bin}(n,1/m)$. Distinct bin counts have <covariance> $-n/m^2$, so they are dependent for $n>0$ and $m>1$. Counts of bins of a specified size are sums of <indicator variables>; their <expectations> follow from the <linearity of expectation>, without any independence between bins.
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