Basic Description

Returns the number of permutations for a given number of objects (with repetitions) that can be selected from the total objects.

Syntax: PERMUTATIONA(number, number-chosen)

The PERMUTATIONA function syntax has the following arguments:

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

PERMUTATIONA uses the following equation:



  • Both arguments are truncated to integers.
  • If numeric arguments are values that are not valid, for example, when the total number is zero (0) and the chosen number is larger than zero (0), PERMUTATIONA returns the #NUM! error value.
  • If numeric arguments use data types that are nonnumeric, PERMUTATIONA returns the #VALUE! error value.



The workbook below shows examples of this function. Inspect them, change existing formulas, or enter your own formulas to learn how the function works. Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

Formula Description Result
=PERMUTATIONA(3,2) Suppose there are 3 objects in the group, [4,5,6]. Using PERMUTATIONA with 2 of the 3 objects, there are 9 ways the numbers can be arranged with repetition: 9

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