# 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.Â 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 66 functions in the 'Math and trigonometry' category.

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