Syntax
MULTINOMIAL(number1, [number2, ...])
| Parameter | Description |
|---|---|
| number1 | Parameter of the MULTINOMIAL function. |
| [number2 | (Optional.) Parameter of the MULTINOMIAL function. |
| ...] | Parameter of the MULTINOMIAL function. |
Examples
Divide into groups
Formula
=MULTINOMIAL(2, 3, 4)
Returns 1,260. There are 1,260 ways to divide 9 people into groups of 2, 3, and 4.
Word arrangements
Formula
=MULTINOMIAL(2, 1, 1)
Returns 12. A 4-letter word with 2 repeated letters (like AABB has 4!/(2!×2!)=6, but this example has groups 2,1,1 giving 4!/(2!×1!×1!)=12).
Simple case
Formula
=MULTINOMIAL(3, 2)
Returns 10. Same as COMBIN(5,3)=10. Dividing 5 items into a group of 3 and a group of 2.
Common Errors
#NUM!
All arguments must be non-negative integers. Negative values return #NUM!.
#VALUE!
Non-numeric arguments produce #VALUE!.
Tips
Extends COMBIN to multiple groups
COMBIN splits items into 2 groups. MULTINOMIAL generalizes to any number of groups: 3 groups, 4 groups, etc.
Anagram counting
To count distinct arrangements of a word like MISSISSIPPI: =MULTINOMIAL(1,4,4,2) = 11!/(1!×4!×4!×2!) = 34,650.
Connects to binomial
MULTINOMIAL(a,b) = COMBIN(a+b, a). The two-argument case is identical to choosing a items from a+b total.
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