We adopt a description of natural languages in terms of strings of crosslinguistically variable syntactic features (parameters), complying with a specified hypothesis of “universal grammar”, and we deal with two problems: first, assessing the statistical significance of language distances calculated on the basis of such features and recently used to reconstruct phylogenetic trees; second, counting the minimal overall number of possible human languages, i.e. of strings satisfying the implicational rules which describe dependencies between parameters of the specified universal grammar. In order to accomplish these tasks, we had to develop a sampling algorithm capable of dealing correctly with such rules. The potential significance of these results for historical and theoretical linguistics is then briefly highlighted.