MULTINOMIAL Function

All versions Math & Trig

The Excel MULTINOMIAL function returns the ratio of the factorial of the sum of values to the product of their individual factorials — the multinomial coefficient used to count arrangements of grouped items.

Quick answer:

=MULTINOMIAL(2,3,4) = 1260

Syntax

=MULTINOMIAL(number1, [number2], ...)

Argument		Description
`number1`	Required	The first value. Each must be non-negative; decimals are truncated.
`number2, ...`	Optional	Up to 254 additional values. MULTINOMIAL uses (sum)! divided by the product of each value's factorial.

How to use it

MULTINOMIAL computes (a + b + c + ...)! / (a! × b! × c! × ...). It counts how many distinct arrangements exist when you have groups of identical items.

=MULTINOMIAL(2,3,4) // 9!/(2!*3!*4!) = 1260

=MULTINOMIAL(1,2,3) // 6!/(1!*2!*3!) = 60

=MULTINOMIAL(2,2) // 4!/(2!*2!) = 6

A classic use is counting distinct letter arrangements of a word with repeated letters, or splitting n items into named groups of fixed sizes. With only two arguments it reduces to a single COMBIN: MULTINOMIAL(k, n-k) = COMBIN(n, k).

Worked check: =MULTINOMIAL(2,3,4) sums to 9, so it computes 9! / (2!×3!×4!) = 362880 / (2×6×24) = 362880 / 288 = 1260.

Try it: interactive demo

Live demo

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example

Result:

Practice workbook

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Frequently asked questions

What does MULTINOMIAL compute?

The multinomial coefficient: the factorial of the sum of all arguments divided by the product of each argument's factorial. =MULTINOMIAL(2,3,4) = 9!/(2!×3!×4!) = 1260.

What is MULTINOMIAL used for?

Counting arrangements of grouped or repeated items — for example distinct orderings of a word's letters when some letters repeat, or dividing items into named groups of set sizes.

How does MULTINOMIAL relate to COMBIN?

With two arguments it equals a combination: MULTINOMIAL(k, n-k) = COMBIN(n, k). MULTINOMIAL generalizes COMBIN to more than two groups.

Can MULTINOMIAL take negative or decimal values?

Negatives return a #NUM! error. Decimals are truncated to whole numbers before the factorials are taken.

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Related functions: FACT · COMBIN · COMBINA · FACTDOUBLE · GCD