PERMUT function

This article describes the formula syntax and usage of the PERMUT function (function: A prewritten formula that takes a value or values, performs an operation, and returns a value or values. Use functions to simplify and shorten formulas on a worksheet, especially those that perform lengthy or complex calculations.) in Microsoft Excel.


Returns the number of permutations for a given number of objects that can be selected from number objects. A permutation is any set or subset of objects or events where internal order is significant. Permutations are different from combinations, for which the internal order is not significant. Use this function for lottery-style probability calculations.


PERMUT(number, number_chosen)

The PERMUT function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

  • Number    Required. An integer that describes the number of objects.
  • Number_chosen    Required. An integer that describes the number of objects in each permutation.


  • Both arguments are truncated to integers.
  • If number or number_chosen is nonnumeric, PERMUT returns the #VALUE! error value.
  • If number ≤ 0 or if number_chosen < 0, PERMUT returns the #NUM! error value.
  • If number < number_chosen, PERMUT returns the #NUM! error value.
  • The equation for the number of permutations is:



Suppose you want to calculate the odds of selecting a winning lottery number. Each lottery number contains three numbers, each of which can be between 0 (zero) and 99, inclusive. The following function calculates the number of possible permutations:

The example may be easier to understand if you copy it to a blank worksheet.

ShowHow do I copy an example?

  1. Select the example in this article. If you are copying the example in Excel Online, copy and paste one cell at a time.
    Important: Do not select the row or column headers.

Selecting an example from Help

Selecting an example from Help

  1. Press CTRL+C.
  2. Create a blank workbook or worksheet.
  3. In the worksheet, select cell A1, and press CTRL+V. If you are working in Excel Online, repeat copying and pasting for each cell in the example.
    Important: For the example to work properly, you must paste it into cell A1 of the worksheet.
  4. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

After you copy the example to a blank worksheet, you can adapt it to suit your needs.

Data Description
100 Number of objects
3 Number of objects in each permutation
Formula Description (Result)
=PERMUT(A2,A3) Permutations possible for the terms above (970200)
Applies to:
Excel 2010, Excel Web App, SharePoint Online for enterprises, SharePoint Online for professionals and small businesses