Excel MULTINOMIAL Function

What is MULTINOMIAL Function in Excel?

The MULTINOMIAL function is one of the math functions of Excel.

It Returns the multinomial of a set of numbers.

It also Calculates the ratio of the factorial of a sum of desired numbers to the product of factorials of those numbers.

We can find this function in Math & trig category of insert function Tab.

How to use MULTINOMIAL function in excel

  1. Click on an empty cell (like F5 )
empty cell in excel

2. Click on fx icon (or press shift+F3)

fx icon in excel

3. In the insert function tab you will see all functions

insert function tab in excel

4. Select math and trig category

5. Select MULTINOMIAL function

6. Then select ok

excel MULTINOMIAL function

7. In the function arguments Tab you will see MULTINOMIAL function

8. Number1: number1,number2,… are 1 to 255 values for which you want the multinomial

9. You will see results in the formula result section

How to use MULTINOMIAL function in excel

Examples of MULTINOMIAL function in Excel

  1. Computing the multinomial coefficient of a set of numbers: Suppose we have a set of numbers {2, 3, 4, 5}. The multinomial coefficient of this set can be computed using the formula “=MULTINOMIAL(2, 3, 4, 5)”.
  2. Computing the probability of a set of outcomes: Suppose we have a set of six possible outcomes, and we want to know the probability of getting two of one type, three of another type, and one of a third type. We can use the MULTINOMIAL function to compute this probability using the formula “=MULTINOMIAL(2, 3, 1)”.
  3. Computing the probability of drawing a certain set of cards from a deck: Suppose we have a deck of cards with four suits (hearts, diamonds, clubs, spades) and we want to know the probability of drawing two hearts, three diamonds, and one club. We can use the MULTINOMIAL function to compute this probability using the formula “=MULTINOMIAL(2, 3, 1)”.
  4. Computing the number of ways to partition a set of items: Suppose we have a set of six items, and we want to know the number of ways to partition them into two groups of three. We can use the MULTINOMIAL function to compute this number using the formula “=MULTINOMIAL(3, 3)”.
  5. Computing the number of ways to arrange a set of items: Suppose we have a set of five items, and we want to know the number of ways to arrange them in a line. We can use the MULTINOMIAL function to compute this number using the formula “=MULTINOMIAL(1, 1, 1, 1, 1)”.
  6. Computing the number of ways to color a set of items: Suppose we have a set of four items, and we want to know the number of ways to color them using three colors. We can use the MULTINOMIAL function to compute this number using the formula “=MULTINOMIAL(1, 1, 1, 2)”.
  7. Computing the number of ways to select a subset of items from a larger set: Suppose we have a set of eight items, and we want to know the number of ways to select four of them. We can use the MULTINOMIAL function to compute this number using the formula “=MULTINOMIAL(4, 4)”.
  8. Computing the number of ways to distribute items among groups: Suppose we have a set of 10 items, and we want to distribute them among three groups so that each group has at least two items. We can use the MULTINOMIAL function to compute the number of ways to do this using the formula “=MULTINOMIAL(2, 2, 6)”.
  9. Computing the number of ways to arrange items with repetitions: Suppose we have a set of three items, and we want to know the number of ways to arrange them in a line with repetitions allowed. We can use the MULTINOMIAL function to compute this number using the formula “=MULTINOMIAL(3)”.
  10. Computing the number of ways to distribute items into bins: Suppose we have a set of six items, and we want to distribute them into two bins so that each bin has at least one item. We can use the MULTINOMIAL function to compute the number of ways to do this using the formula “=MULTINOMIAL(1, 5)”.

Example 1:

How to use MULTINOMIAL function in excel

You can see examples of MULTINOMIAL function below:

Examples of MULTINOMIAL function in Excel
multinomial(A2,B2,C2) ----->>>>answer is  60

multinomial(A3,B3,C3) ----->>>>answer is  1260

multinomial(A4,B4,C4) ----->>>>answer is  27720

multinomial(A5,B5,C5) ----->>>>answer is  630630

multinomial(A6,B6,C6) ----->>>>answer is  14702688

Excel’s MULTINOMIAL Function: What You Need to Know

Excel’s MULTINOMIAL function is a statistical function that calculates the multinomial coefficient of a set of numbers. This function can be used to solve a wide range of combinatorial problems, including probability calculations, arrangements, and distributions.

The MULTINOMIAL function takes a series of arguments as inputs, each representing the number of times an element appears in a sample. For example:





=MULTINOMIAL(2, 3, 1)

This formula will calculate the multinomial coefficient for a sample containing two elements of one type, three elements of another type, and one element of a third type.

Calculating Multinomial Coefficients with Excel’s MULTINOMIAL Function

The MULTINOMIAL function in Excel can be used to calculate the multinomial coefficient of a set of numbers. This coefficient represents the number of ways in which a set of items can be partitioned into groups.

For instance, the following formula calculates the multinomial coefficient for the set {2, 3, 4}:





=MULTINOMIAL(2, 3, 4)

The result of this calculation is 1260, which represents the number of ways in which a set of nine items can be partitioned into three groups containing two, three, and four items, respectively.

Practical Applications of Excel’s MULTINOMIAL Function in Data Analysis

Excel’s MULTINOMIAL function has numerous practical applications in data analysis. One common use case is to compute the multinomial distribution of a set of outcomes. This distribution can be used to predict the probabilities of various combinations of outcomes.

For example, let’s suppose we have a set of six possible outcomes, labeled A, B, C, D, E, and F. We want to know the probability of selecting three A’s, two B’s, and one C. We can use the MULTINOMIAL function to compute this probability as follows:





=MULTINOMIAL(3, 2, 1)/720

The result of this calculation is approximately 0.0486, or 4.86%.

Syntax and Usage of Excel’s MULTINOMIAL Function

The syntax for the MULTINOMIAL function in Excel is as follows:





=MULTINOMIAL(number1,[number2],...)

The arguments to this function are the numbers that represent the frequency of each element in the sample. The function returns the multinomial coefficient of the sample.

For example, let’s suppose we have a sample with three elements: A, B, and C. The sample contains two A’s, three B’s, and one C. We can calculate the multinomial coefficient of this sample using the following formula:





=MULTINOMIAL(2, 3, 1)

The result of this calculation is 60, which represents the number of ways in which the items in the sample can be arranged.

Using Non-Integer Values with Excel’s MULTINOMIAL Function

Excel’s MULTINOMIAL function can only accept integers as its arguments. If you try to pass a non-integer value to the function, it will return a #VALUE! error.

However, you can use other functions or techniques to work around this limitation. For example, you can multiply all of the arguments by a common factor to convert them into integers. Alternatively, you can use Excel’s ROUND or INT functions to round the arguments to the nearest integer.

For instance, the following formula uses the ROUND function to compute the multinomial coefficient of a set of non-integer values:





=MULTINOMIAL(ROUND(2.5), ROUND(3.7), ROUND(1.2))

The result of this calculation is 90, which represents the number of ways in which a set of eight items can be partitioned into three groups containing three, four, and one item, respectively.

How Excel’s MULTINOMIAL Function Handles Large Sets of Numbers

Excel’s MULTINOMIAL function can handle large sets of numbers, but you may experience performance issues if you pass a very large number of arguments to the function. As a general rule, you should avoid passing more than 20 or 30 arguments to the function.

For example, the following formula calculates the multinomial coefficient for a set of 10 numbers:





=MULTINOMIAL(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)

The result of this calculation is 184756, which represents the number of ways in which a set of 55 items can be partitioned into 10 groups.

The Impact of Negative Numbers on Excel’s MULTINOMIAL Function

If you pass negative numbers to Excel’s MULTINOMIAL function, it will return a #NUM! error. This is because the function can only handle positive integers as its arguments.

For example, the following formula returns an error because it includes a negative number:





=MULTINOMIAL(2, -3, 4)

To avoid this error, ensure that all of the arguments passed to the MULTINOMIAL function are positive integers.

Handling Missing or Empty Cells with Excel’s MULTINOMIAL Function

Excel’s MULTINOMIAL function ignores missing or empty cells in a range. If you pass a range with missing cells to the function, it will only use the non-missing cells when calculating the multinomial coefficient.

For example, suppose we have a sample with three elements: A, B, and C. The sample contains two A’s and three C’s, but there is a missing cell where the second B should be. We can calculate the multinomial coefficient of this sample using the following formula:





=MULTINOMIAL(2, 0, 3)

The result of this calculation is 10, which represents the number of ways in which the items in the sample can be arranged.

Excel’s MULTINOMIAL Function Compared to Other Statistical Functions

Excel’s MULTINOMIAL function is a specialized statistical function that calculates the multinomial coefficient of a set of numbers. It is similar to other combinatorial functions in Excel, such as COMBIN and PERMUT, which calculate the number of combinations and permutations of a set of items.

However, the MULTINOMIAL function is specifically designed for cases where items can be grouped into multiple categories. It is also more flexible than the COMBIN or PERMUT functions, which only work with two categories (e.g., selecting x items out of y total).

Using Excel’s MULTINOMIAL Function for Probability Calculations

Excel’s MULTINOMIAL function can be used to calculate probabilities for complex events involving multiple outcomes. For example, suppose we have a set of six possible outcomes: A, B, C, D, E, and F. We want to know the probability of selecting three A’s, two B’s, and one C.

We can use the following formula to calculate the probability of this event:





=MULTINOMIAL(3, 2, 1)/720

The result of this calculation is approximately 0.0486, or 4.86%.

Finding the Number of Ways to Arrange Items with Excel’s MULTINOMIAL Function

Excel’s MULTINOMIAL function can be used to find the number of ways in which a set of items can be arranged. This is because arranging items involves partitioning them into groups based on their order.

For example, suppose we have a set of six items: A, B, C, D, E, and F. We want to know the number of ways in which these items can be arranged.

We can use the following formula to calculate this number:





=MULTINOMIAL(1, 1, 1, 1, 1, 1)

The result of this calculation is 720, which represents the number of ways to arrange six items.

Solving Combinatorics Problems with Excel’s MULTINOMIAL Function

Excel’s MULTINOMIAL function can be used to solve a wide range of combinatorics problems, including arrangements, distributions, and selections. These problems involve counting the number of ways in which items can be partitioned into different groups based on various criteria.

For example, let’s suppose we have a set of eight items: A, B, C, D, E, F, G, and H. We want to know the number of ways to divide these items into two groups of three and one group of two.

We can use the following formula to calculate the number of ways to partition these items:





=MULTINOMIAL(3, 3, 2)/2

The result of this calculation is 420, which represents the number of ways to partition eight items into groups of three, three, and two.

Calculating the Number of Ways to Color Items with Excel’s MULTINOMIAL Function

Excel’s MULTINOMIAL function can be used to calculate the number of ways in which a set of items can be colored. This involves partitioning the items into groups based on their color.

For example, suppose we have a set of four items: A, B, C, and D. We want to know the number of ways in which these items can be colored using three different colors.

We can use the following formula to calculate this number:





=MULTINOMIAL(2, 1, 1)/2

The result of this calculation is 6, which represents the number of ways to color four items using three different colors.

Using Excel’s MULTINOMIAL Function to Find the Number of Ways to Select Items

Excel’s MULTINOMIAL function can also be used to find the number of ways in which items can be selected from a larger set. This involves partitioning the larger set into smaller subsets based on the number of items selected.

For example, let’s suppose we have a set of eight items: A, B, C, D, E, F, G, and H. We want to know the number of ways to select four items from this set.

We can use the following formula to calculate this number:





=MULTINOMIAL(4, 4)/24

The result of this calculation is 70, which represents the number of ways to select four items from a set of eight.

Distributing Items Among Groups with Excel’s MULTINOMIAL Function

Excel’s MULTINOMIAL function can also be used to distribute items among different groups or categories. This involves partitioning the items into subsets based on the number of items in each group.

For example, let’s suppose we have a set of nine items: A, B, C, D, E, F, G, H, and I. We want to know the number of ways to distribute these items into three groups containing two, three, and four items, respectively.

We can use the following formula to calculate this number:





=MULTINOMIAL(2, 3, 4)/2

The result of this calculation is 1260, which represents the number of ways to distribute nine items into three groups containing two, three, and four items, respectively.

Using Excel’s MULTINOMIAL Function to Distribute Items into Bins

Excel’s MULTINOMIAL function can be used to distribute items into different bins or categories. This involves partitioning the items into subsets based on the number of items in each bin.

For example, let’s suppose we have a set of 10 items: A, B, C, D, E, F, G, H, I, and J. We want to know the number of ways to distribute these items into four bins containing two, three, three, and two items, respectively.

We can use the following formula to calculate this number:





=MULTINOMIAL(2, 3, 3, 2)/((2!)*(3!)*(3!)*(2!))

The result of this calculation is 1260, which represents the number of ways to distribute ten items into four bins containing two, three, three, and two items, respectively.

Combining Excel’s MULTINOMIAL Function with Other Functions

Excel’s MULTINOMIAL function can be combined with other functions to solve more complex problems. For example, you could use the SUMPRODUCT function to find the sum of multiple multinomial coefficients.

As another example, let’s suppose we have a set of six items: A, B, C, D, E, and F. We want to know the number of ways to distribute these items into two bins containing three items each, and then color each bin using one of three different colors.

We can use the following formula to calculate this number:





=SUMPRODUCT(MULTINOMIAL({3,3}),MULTINOMIAL({1,1,1}))

The result of this calculation is 540, which represents the number of ways to distribute six items into two bins containing three items each, and then color each bin using one of three different colors.

The Importance of Argument Order in Excel’s MULTINOMIAL Function

The order of the arguments passed to Excel’s MULTINOMIAL function is important. This is because the function treats each argument as representing a specific item or category in the sample being analyzed.

For example, let’s suppose we have a sample with four items: A, B, C, and D. We want to know the number of ways to arrange these items such that A comes before B, and C comes before D.

We can use the following formula to calculate this number:





=MULTINOMIAL(1, 1, 2)

The result of this calculation is 6, which represents the number of ways to arrange four items with two distinct groups.

Common Mistakes to Avoid When Using Excel’s MULTINOMIAL Function

One common mistake when using Excel’s MULTINOMIAL function is passing non-integer values to the function, which will result in a #VALUE! error. Another common mistake is passing negative numbers to the function, which will result in a #NUM! error.

Another mistake to avoid is passing too many arguments to the function, which can cause performance issues or lead to incorrect results. As a general rule, you should avoid passing more than 20 or 30 arguments to the function.

Availability of Excel’s MULTINOMIAL Function in Different Versions

Excel’s MULTINOMIAL function is available in all versions of Microsoft Excel, including Excel 2019, Excel 2016, Excel 2013, Excel 2010, and earlier versions. However, the syntax and usage of the function may vary slightly between different versions. It is important to consult the documentation for your version of Excel to ensure that you are using the function correctly.

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