I am faced with a problem in combinatorics while trying to set up a pool. Instead of explaining my real problem, I prefer to give you a simplified example: Say I am given a population of N persons of varying height ##h_i##. The height of each person ##i## in the population is known to me. Now I want to set up a sample of n persons so that the mean value of the height has on average a predefined value which is different from the grand mean of the overall population but otherwise I want the two populations to be as similar as possible. Especially, I don't want to introduce a hard cutoff. I thought about Kullback Leibler entropy maximization, and this works well if it were possible to sample the same person repeatedly. But how do you proceed if a person can only be drawn one time?