 The probability that the th integer randomly chosen from will repeat at least one previous choice equals above.The expected total number of times a selection will repeat a previous selection as such integers are chosen equals

In an alternative formulation of the birthday problem, one asks the "average" number of people required to find a pair with the same birthday.If we consider the probability function Pr[ people have at least one shared birthday], this "average" is determining the mean of the distribution, as opposed to the customary formulation, which asks for the median.