How to use the MULTINOMIAL function
What is the MULTINOMINAL function?
The MULTINOMIAL function calculates the ratio of the factorial of a sum of values to the product of factorials.
What is the sum of values?
Summarize is when you add numbers using addition and the result is the sum or total.
For example, lets use the numbers 2, 3 and 4.
2 + 3 + 4 = 9
The sum is 9.
What is the factorial of a sum of values?
The factorial of a number n is the product of all positive integers less than or equal to n, and is represented by n!
The factorial of a number n is defined as:
n! = n * (n-1) * (n-2) * ... * 3 * 2 * 1
In other words, the factorial of a number n is the product of all positive integers less than or equal to n.
Some examples:
1! = 1
2! = 2 * 1 = 2
3! = 3 * 2 * 1 = 6
4! = 4 * 3 * 2 * 1 = 24
5! = 5 * 4 * 3 * 2 * 1 = 120
0! = 1
The factorial function grows very quickly as n increases. Factorials are useful in combinatorics for counting permutations and combinations.
Using the example that returned the sum of 9, the factorial becomes 9!
9*8*7*6*5*4*3*2*1 = 362880
What is the product of values?
Multiplication is one of the basic arithmetic operations, along with addition, subtraction, and division. Multiplication involves taking two numbers, called factors or terms, and combining them to get a product.
It is denoted by the multiplication symbol * or x. For example: 5 * 3 = 15
What is the factorial of a product of values?
The factorial of a product is equal to the product of the individual factorials.
For example:
(2*3*4)! = 2! * 3! * 4! = 2 * 6 * 24= 288
What is the ratio of the factorial of a sum of values to the product of factorials?
Proceeding with the values above 2,3, and 4 we get 362880 / 288 equals 1260.
What is the ratio?
A ratio shows the relative size of two or more values. It is one number divided by another. A ratio compares two quantities using division.
Ratios can be written as fractions, with the numerator and denominator representing the values being compared. Use / in an Excel formula to perform a division and create a ratio.
What functions use the factorial in Excel?
| Function | Description |
|---|---|
| MULTINOMIAL(n1, n2, ...) | Returns the ratio of the factorial of a sum of values to the product of factorials. |
| FACT(number) | Returns the factorial of the provided number. |
| FACTDOUBLE(number) | Returns the double factorial of the provided number. |
Excel Function Syntax
MULTINOMIAL(number1, [number2], ...)
Arguments
| number1 | Required. The number for which you want to calculate the multinomial. |
| [number2] | Optional. Up to 254 additional numbers. |
MULTINOMIAL function example
Formula in cell D3:
The value is calculated like this:
MULTINOMIAL function not working
MULTINOMIAL returns
- #VALUE! if argument is nonumeric.
- #NUM! if argument is less than 0 (zero).
Functions in 'Math and trigonometry' category
The MULTINOMIAL function function is one of many functions in the 'Math and trigonometry' category.
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