Random samples without replacement are extracted from a distributed set of items by leveraging techniques for aggregating sampled subsets of the distributed set. This provides a uniform random sample without replacement representative of the distributed set, allowing statistical information to be gleaned from extremely large sets of distributed information. Subset random samples without replacement are extracted from independent subsets of the distributed set of items. The subset random samples are then aggregated to provide a uniform random sample without replacement of a fixed size that is representative of a distributed set of items of unknown size. In one instance, a multivariate hyper-geometric distribution is sampled by breaking up the multivariate hyper-geometric distribution into a set of univariate hyper-geometric distributions. Individual items of a uniform random sample without replacement are then determined utilizing a normal approximation of the univariate hyper-geometric distributions and a finite population correction factor.