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Math function
MULTINOMIAL
Returns the multinomial of a set of numbers: the factorial of the sum divided by the product of the factorials.
Rarely usedDifficulty 1400 · AdvancedUsage rank #353 of 520
When to use it
The multinomial coefficient: (sum of the numbers)! divided by the product of each number's factorial. Ways to split a group into labeled subgroups of given sizes.
The shape of it
- Syntax
=MULTINOMIAL(number1, [number2], ...)
Worked examples
Three groups
=MULTINOMIAL(2,3,4) → 1260
Ways to split nine people into groups of 2, 3, and 4.
All singletons
=MULTINOMIAL(1,1,1) → 6
Three distinct items in order.
Two groups
=MULTINOMIAL(3,2) → 10
Same as COMBIN(5,3).
Worth knowing
- With two arguments it equals COMBIN(a+b,a).
- Non-integers are truncated.
- Word arrangements with repeated letters: MULTINOMIAL of the letter counts.
Where it goes wrong
- #NUM! for negative arguments.
- Large inputs overflow.
Related
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