What does multinomial mean?
Multinomial is a technical mathematics and probability term meaning that an operation, expression, or distribution involves more than two factors or categories. Its best-known uses are the multinomial theorem, which expands a power of a sum such as (x + y + z)^n into a collection of terms, and the multinomial distribution, which generalizes the binomial distribution to outcomes with more than two possible values. A multinomial coefficient counts arrangements or selections when items are divided among several groups. The word belongs to formal mathematical and statistical writing rather than everyday English, so its exact sense depends on context. It also provides a useful distinction: a binomial concerns two categories, while a multinomial concerns any larger set. Although less familiar than binomial, the term is precise and foundational in combinatorics, probability, algebra, and related fields.
Denoting a mathematical expression, coefficient, theorem, or probability distribution involving more than two factors, terms, or categories.
"The researchers fitted a multinomial model to the observed frequencies."
In probability, the term is usually reserved for distributions or models with more than two mutually exclusive outcomes.
A mathematical expression or coefficient arising from the expansion of a power of a sum containing two or more terms.
"Each multinomial in the expansion represents one possible combination of powers."
The noun is used chiefly in advanced mathematical contexts and is less common in general prose.
The plural is uncommon in general writing but can refer to multiple distinct multinomial expressions or coefficients.
"The resulting multinomials have different coefficients."
It is the many-category version of the familiar binomial, taking probability and algebra beyond a simple choice between two outcomes.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does multinomial come from?
The English mathematical term combines the Latin prefix multi-, meaning “many,” with the combining element -nomial, as found in binomial. It developed as mathematicians generalized binomial nomenclature to expressions and expansions involving more than two factors or categories. Parallel mathematical formations include monomial, binomial, and polynomial, with binomial and polynomial being especially close in terminology and meaning.
How multinomial is actually used
This is formal mathematical and statistical terminology rather than everyday vocabulary. In probability, it specifically generalizes the binomial distribution to experiments with more than two possible outcomes.
Easily confused with multinomial
A binomial expression or distribution involves two categories or factors, whereas a multinomial one involves more than two.