PERMUT Function

The Excel PERMUT function calculates the permutation without repetition when a certain number of items are taken from the entire set of items. This versatile function is categorized under the Excel Statistical function and was appended to Excel 2007. The hidden quality of the PERMUT function is its resilience to errors when provided with negative arguments. It also works perfectly with arrays and dynamic ranges, performs exceptionally in rank analysis, and effectively combines with other functions like SEQUENCE, and COMBIN to tackle the complex permutation calculations with precision.

Compatibility

This advanced Excel function is compatible with the following versions of MS Excel

Excel for Microsoft 365
Excel for Microsoft 365 for Mac
Excel for the web
Excel 2024
Excel 2024 for Mac
Excel 2021
Excel 2021 for Mac
Excel 2019
Excel 2016
Excel 2013
Excel 2010
Excel 2007

Syntax

The syntax of the PERMUT function is as follows −

=PERMUT(number, number_chosen)

Arguments

You can use the following arguments with the PERMUT function −

Argument	Description	Required/ Optional
Number	An integer value which shows the number of objects.	Required
Number_chosen	An integer value that permits users about the total number of objects residing in every permutation.	Required

Points to Remember

The equation for the number of permutations is −

$$\mathrm{P_{k,n}\:=\:\frac{n!}{\left ( n\:-\:k \right )!}}$$

Both arguments contain a decimal value, it is truncated to integers.
If either of the arguments contains a non-numeric value, then the PERMUT function returns the #VALUE! error.
If number ≤ 0 or if number_chosen contains negative value, then the PERMUT function returns the #NUM!.
If number_chosen is greater than number, then the PERMUT function returns the #NUM! error.

Examples of PERMUT Function

Practice the following examples to learn the use of the PERMUT function in Excel.

Example 1: How to calculate the permutation when the number of balls is 6 chosen from the total of 25 balls in the play zone?

In this example, the PERMUT function is applied to determine the number of permutations for P(25, 6).

Solution

First, deliberate an Excel sheet, select cell B2, type the formula =PERMUT(25,6), and hit the Enter tab.

Therefore, the result is 127512000.

Example 2

If either of the arguments contains a non-numeric value, then the PERMUT function returns the #VALUE! error

Solution

First, switch to the "example 2 and example 3" worksheet and write the formula =PERMUT("sw",12) in the B2 cell, and hit the Enter tab. In this expression, the Number contains the text value which is invalid.

Hence, the PERMUT function yields a #VALUE! error.

Example 3

If number ≤ 0 or if number_chosen contains negative value, then the PERMUT function returns the #NUM!.

Solution

Select a cell B3 and type the formula =PERMUT(-12,3) and hit the Enter tab.

Therefore, the PERMUT function generates the #NUM! error as the Number contains a negative value which is inaccurate.

Download Practice Sheet

You can download and use the sample data sheet to practice the PERMUT function.

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