MULTINOMIAL
Returns the multinomial coefficient: the ratio of the factorial of the sum of values to the product of factorials of each value.
MULTINOMIAL(number1, [number2], ...)Arguments
number1The first non-negative integer.number2Optional. Additional non-negative integers (up to 255).(optional)
=MULTINOMIAL(2,3,4)9! / (2! × 3! × 4!) = 1260
=MULTINOMIAL(1,2,3)6! / (1! × 2! × 3!) = 60
- •Returns #NUM! if any argument is negative
- •Returns #VALUE! if any argument is non-numeric
- •Used in combinatorics, probability and polynomial expansions
- •Passing a negative number as any argument, which returns a #NUM! error since multinomial coefficients are only defined for non-negative integers
- •Confusing MULTINOMIAL with COMBIN or PERMUT - MULTINOMIAL generalizes the idea of counting arrangements to groups of multiple distinct categories, rather than simple two-outcome combinations or permutations
- •Expecting the result to grow slowly - multinomial coefficients can become astronomically large very quickly as the input numbers increase, since they're built from factorials
COMBINCalculates combinations for a simpler two-category case, of which MULTINOMIAL is a generalization to multiple categories.FACTUsed internally in the mathematical formula behind MULTINOMIAL, since multinomial coefficients are calculated using factorials of each argument and their sum.PERMUTCalculates permutations where every item is distinct, a different counting scenario than MULTINOMIAL's grouped-items case.Why does MULTINOMIAL return a #NUM! error?
One of the arguments is negative - multinomial coefficients are only defined for non-negative integers.
What does MULTINOMIAL actually calculate?
It calculates how many distinct ways a set of items can be arranged when divided into groups of specified sizes - the factorial of the total count divided by the product of each group's factorial.
Why did MULTINOMIAL return such a huge number?
Multinomial coefficients grow extremely fast because they're built from factorials - even moderately sized inputs can produce enormous results.
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