I have a known multinomial distribution of a population due to a census. I want to compare a sample with this population. I want to know the probability that the same ranking of the classes of the multinomial is observed in the sample as in the population. Example: Assume there are 20 brands of wine. We know the market share of each brand. What is the probability of observing the most frequent brand as a the most frequent brand in a sample AND of the second most frequent brand as the second most frequent brand in the sample and so on up to the k-most frequent brand.