The study of the numbers of ways of selecting, or arranging, objects from a finite set. Its main applications in the theory of probability are in calculating the probability of an event such as r of the objects chosen having a particular property, or the probability of a sequence of events with a particular property. See also binomial distribution; hypergeometric distribution; negative binomial distribution.
Combinatorial results often involve factorials and binomial coefficients. For example, the probability that, in a random deal of 13 cards from a normal pack, Player A receives 13 spades isand the probability that in a random deal to four players, each player receives 13 cards of the same suit is