A Method of Sampling with Equal or Unequal Probabilities Without Replacement

The purpose of this article is to give a method of computing the mth element in the ordered set of ( ) samples arranged lexicographically without enumerating the whole set. A selection procedure with preassigned probability of selection of population units without replacement is suggested. The method has several interesting applications in the areas of simulation studies and in problems of obtaining repeated samples with some number of units common in the repeated sample.