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MULTINOMIAL

The MULTINOMIAL function in Google Sheets calculates the multinomial of a set of numbers. The multinomial of a set of values is the product of factorials of the values divided by the factorial of the sum of the values. This function is useful when working with combinations of sets of values.

Usage

Use the MULTINOMIAL formula with the syntax shown below, it has 2 required parameters:

=MULTINOMIAL(value1, value2)
Parameters:
  1. value1 (required):
    A set of values to be used in the multinomial calculation. There must be at least 2 values in the set.
  2. value2 (required):
    Additional sets of values to be used in the multinomial calculation. There can be up to 255 additional sets.

Examples

Here are a few example use cases that explain how to use the MULTINOMIAL formula in Google Sheets.

Calculating the number of possible outcomes

Suppose you have a set of 5 items and want to know how many possible combinations of 2 items can be created from that set. You can use the MULTINOMIAL function to calculate this by providing the values 3 and 2 as the two sets of values.

Calculating the probability of outcomes

If you know the total number of possible outcomes and the number of desired outcomes, you can use the MULTINOMIAL function to calculate the probability of getting the desired outcomes. For example, if you have a set of 6 items and want to know the probability of getting 2 specific items when choosing 4 items, you can use the MULTINOMIAL function to calculate this.

Calculating the number of ways to distribute items

Suppose you have a set of 10 identical items and want to distribute them among 3 people. You can use the MULTINOMIAL function to calculate the number of ways to distribute the items by providing the values 4, 3, and 3 as the sets of values.

Common Mistakes

MULTINOMIAL not working? Here are some common mistakes people make when using the MULTINOMIAL Google Sheets Formula:

Incorrect number of arguments

The MULTINOMIAL formula requires at least two arguments separated by commas, and can accept up to 255 arguments. Check that the correct number of arguments have been included.

Invalid input type

The MULTINOMIAL formula only works with numeric values. Check that the input values are numbers or can be interpreted as numbers.

Non-integer input value

The MULTINOMIAL formula only works with integer values. If any input value is not an integer, the formula will return an error. Use the ROUND function to convert non-integer values to integers.

Value is negative

The MULTINOMIAL formula only works with positive values. If any input value is negative, the formula will return an error. Check that the input values are positive.

Value is zero

The MULTINOMIAL formula only works with positive values. If any input value is zero, the formula will return an error. Check that the input values are positive.

Related Formulas

The following functions are similar to MULTINOMIAL or are often used with it in a formula:

  • COMBIN

    The COMBIN function calculates the number of combinations for a given number of items. A combination is a way of selecting items from a larger set where order does not matter. This function is commonly used in probability and statistics.

  • PERMUT

    The PERMUT function returns the number of permutations of a set of objects. A permutation is a way of arranging objects in a specific order. The function takes two arguments: n, the total number of objects, and k, the number of objects to arrange. The result is the number of possible permutations. This function is commonly used in combinatorics and probability theory.

  • RANDARRAY

    The RANDARRAY formula is used to create an array of random numbers between 0 and 1. The size of the array is determined by the number of rows and columns specified in the formula.

  • SUM

    The SUM function in Google Sheets adds up a range of numbers. This function is most commonly used to sum the values in a range of cells.

Learn More

You can learn more about the MULTINOMIAL Google Sheets function on Google Support.