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.



Number     is an integer that describes the number of objects.

Number_chosen     is 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 to copy an example

  • Create a blank workbook or worksheet.
  • Select the example in the Help topic.

 Note   Do not select the row or column headers.

Selecting an example from Help

Selecting an example from Help
  • Press CTRL+C.
  • In the worksheet, select cell A1, and press CTRL+V.
  • 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.
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 2003