Some Properties of Pascal Distribution for Finite Population

This note deals with a waiting time problem. The probability distribution of the number of independent random drawings, if the probability of success at a single drawing is constant, is well known and is usually referred to as Pascal distribution. It may be looked upon as a probability distribution of the number of drawings from an infinite population. The present note is concerned with the generalization of this result to the case of drawings (without replacement) from a finite population.