Editing Multinomial distribution (section)

=== Example ===

Suppose that in a three-way election for a large country, candidate A received 20% of the votes, candidate B received 30% of the votes, and candidate C received 50% of the votes.  If six voters are selected randomly, what is the probability that there will be exactly one supporter for candidate A, two supporters for candidate B and three supporters for candidate C in the sample?

''Note: Since we’re assuming that the voting population is large, it is reasonable and permissible to think of the probabilities as unchanging once a voter is selected for the sample.  Technically speaking this is sampling without replacement, so the correct distribution is the [[Hypergeometric distribution#Multivariate hypergeometric distribution|multivariate hypergeometric distribution]], but the distributions converge as the population grows large in comparison to a fixed sample size''<ref>{{Cite web |title=probability - multinomial distribution sampling |url=https://stats.stackexchange.com/a/335239/307588 |access-date=2022-07-28 |website=Cross Validated |language=en}}</ref>''.''

: <math> \Pr(A=1,B=2,C=3) = \frac{6!}{1! 2! 3!}(0.2^1) (0.3^2) (0.5^3) = 0.135 </math>