The matching problem

Tables of the exact distributions of number of matches are given for small decks having the same number of cards in each suit. Several approximate distributions are considered for use with larger decks, and some indication of the goodness of the approximations is given.The calculations for this paper were done while the writer was working on a project sponsored by funds from the Ford Foundation. The writer wishes to express his gratitude to Dr. Frederick Mosteller for his constant help and encouragement during the writing of this paper.