The world's linguistic diversity is large, probably much larger than many linguists would want to admit. Dealing with this diversity is a central objective for worldwide crosslinguistic investigations. This article argues that to deal with diversity it is extremely fruitful to work with probable structures instead of possible structures, with models instead of theories, and with levels of justification instead of right or wrong. This is illustrated with the order of demonstrative, numeral, adjective, and noun within a complex noun phrase. Different NP-internal orders have strongly differing frequencies among the world's languages. Various models to capture these frequencies are proposed and compared to each other, and it will be argued that very simple models are sufficient. For example, a highly adequate model only refers to the fact that noun and adjective tend to occur together, nouns and demonstratives prefer to occur at the phrase boundary, and noun-adjective order is slightly more frequent than adjective-noun order. The same approach will also be used to model sentence word order frequencies, including areal preferences as random effects. Using such probabilistic models allows for a new take on typological explanations. In and of itself, a probabilistic model is no explanation. However, a well-fitting model instantiates a reformulation of the original phenomenon to be explained into smaller, more tractable phenomena.