# Statistics Dictionary

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### Multinomial Distribution

A multinomial distribution is the probability distribution of the outcomes from a multinomial experiment . The multinomial formula defines the probability of any outcome from a multinomial experiment.

Multinomial Formula. Suppose a multinomial experiment consists of n trials, and each trial can result in any of k possible outcomes: E1, E2, . . . , Ek. Suppose, further, that each possible outcome can occur with probabilities p1, p2, . . . , pk. Then, the probability (P) that E1 occurs n1 times, E2 occurs n2 times, . . . , and Ek occurs nk times is

P = [ n! / ( n1! * n2! * ... nk! ) ] * ( p1 n1 * p2 n2 * . . . * pk nk )

where n = n1 + n1 + . . . + nk.

Sample problems that illustrate the use of the multinomial formula can be found in the Stat Trek's Statistics Tutorial in the lesson on the multinomial distribution .