Suppose that an experiment can result in one of r possible outcomes, the ith outcome having probability pi, i = 1,...,, E P = 1.

If n of these experiments are performed, and if the outcome of any one of the n does not affect the outcome of the other n 1 experiments, then show that the probability that the first outcome appears x, times, the second x2 times, and the rth x, times is n! x11x!...x,! Pipp when x1 + x2 + + x = n This is known as the multinomial distribution.