# MULTINOMIAL

Formulas / MULTINOMIAL
Calculate the ratio of the factorial of a sum of values to the product of factorials.
`MULTINOMIAL(number1, [number2], [number3],...)`
• number1 - required argument
• number2 - [OPTIONAL] additional argument

## Examples

• `=MULTINOMIAL(2, 3, 4)`

The Multinomial function can be used to calculate the ratio of the factorial of the sum of two or more numbers to the product of the factorials of each of the numbers. For instance, this returns the ratio of the factorial of the sum of 2, 3, and 4 to the product of the factorials of 2, 3, and 4, which is 362880 to 288.

• `=MULTINOMIAL(2, 3, 4, 5)`

Multinomial function can also be used to calculate the ratio of the factorial of the sum of two or more numbers to the product of the factorials of each of the numbers in a different way. For example, the formula returns the ratio of the factorial of the sum of 2, 3, 4, and 5 to the product of the factorials of 2, 3, 4, and 5, which is 39916800 to 1440.

• `=MULTINOMIAL(2, 3, 4, 5, 6)`

The Multinomial function can also be used to calculate the ratio of the factorial of the sum of two or more numbers to the product of the factorials of each of the numbers in a more complicated way. For instance, when using the formula, the ratio of the factorial of the sum of 2, 3, 4, 5, and 6 to the product of the factorials of 2, 3, 4, 5, and 6 is 479001600 to 20160.

## Summary

The MULTINOMIAL function returns the ratio of a sum of factorials to the product of factorials for a set of given numbers. The first argument is required, while the additional numbers are optional.

• The MULTINOMIAL function takes a required argument and any number of optional arguments.
• The function returns the ratio of the factorial of a sum of values to the product of factorials.
• It is important to note that the arguments must be valid numerical values.

What is the MULTINOMIAL function?
The MULTINOMIAL function calculates the ratio of the factorial of a sum of values to the product of factorials.
What is the first argument of the MULTINOMIAL function?
The first argument is required.
Are there any subsequent arguments for the MULTINOMIAL function?
Yes, the subsequent arguments are optional.
What are some examples of how to use the MULTINOMIAL function?
Here are some examples of how to use the MULTINOMIAL function:
• To calculate the ratio of the factorial of 10 to the product of factorials of 5 and 2, use the MULTINOMIAL function: =MULTINOMIAL(10,5,2)
• To calculate the ratio of the factorial of 15 to the product of factorials of 5, 3 and 2, use the MULTINOMIAL function: =MULTINOMIAL(15,5,3,2)