Bootstrap count vectors
= Bootstrap count vectors
{title2=$N_1+\cdots+N_n=n$}
An unordered nonparametric <bootstrap sample> from $n$ distinct observations is specified by its $n$ nonnegative multiplicities. <Stars and bars> gives $\binom{2n-1}{n}$ such vectors. They are not equiprobable: a vector has <probability> $n!/(n^n\prod_iN_i!)$, because this counts its ordered sequences of sampled indices.