## DEFINITION of 'Multinomial Distribution '

A distribution that shows the likelihood of the possible results of a experiment with repeated trials in which each trial can result in a specified number of outcomes that is greater than two. A multinomial distribution could show the results of tossing two dice, because each die can land on one of six possible values. By contrast, the results of a coin toss would be shown using a binomial distribution because there are only two possible results of each toss, heads or tails.

## BREAKING DOWN 'Multinomial Distribution '

Two additional key characteristics of a multinomial distribution are that the trials it illustrates must be independent (e.g., in the dice experiment, rolling a five does not have any impact on the number that will be rolled next) and the probability of each possible result must be constant (e.g., on each roll, there is a one in six chance of any number on the die coming up).