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MULTINOMIAL Function
Summary
The Excel MULTINOMIAL function calculates the multinomial coefficient, which is the ratio of the factorial of the sum of given numbers to the product of their individual factorials. This is essential for combinatorial calculations in probability and statistics.
Syntax
MULTINOMIAL(number1, [number2], ...)Parameters
| Parameter | Type | Required | Description |
|---|---|---|---|
| number1 | Number |
Yes | First positive integer (required) |
| number2, ... | Number |
No | Additional positive integers (optional, up to 254 more for total of 255) |
Using the MULTINOMIAL Function
MULTINOMIAL is valuable for statistical analysis, particularly when working with multinomial probability distributions, counting combinations with repetition, and advanced combinatorial problems where traditional combinations don't apply.
Common MULTINOMIAL Examples
Basic Multinomial Calculation
=MULTINOMIAL(2,3,4)Calculates (2+3+4)! / (2!×3!×4!) = 362880 / 288 = 1260. Represents ways to divide 9 distinct items into groups of 2, 3, and 4.
Simple Binomial Case
=MULTINOMIAL(5,3)Equivalent to C(8,5) or C(8,3) = 56 ways to choose 5 items from 8.
Single Group Scenario
=MULTINOMIAL(4)Returns 4! / 4! = 1 (single permutation case).
Frequently Asked Questions
Common Errors and Solutions
#VALUE!
Cause: Any argument is non-numeric
Solution: Ensure all arguments are valid numbers
#NUM!
Cause: Any argument is negative or zero
Solution: Use only positive integers ≥ 0
#DIV/0!
Cause: Zero factorial in denominator (rare)
Solution: Avoid zero arguments or handle separately
Notes
- Maximum 255 arguments allowed
- All arguments must be positive integers
- Result can be very large for bigger numbers
- Useful in multinomial theorem applications
Compatibility
Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365
Not available in: Excel 2003 and earlier
Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+