How to use PERMUTATIONA Function in Excel

The PERMUTATIONA function returns the number of permutations for a given number of objects (with repetitions) that can be selected from the total objects.

PERMUTATIONA uses the following equation:

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.

Example: Let’s look at some Excel PERMUTATIONA function examples and explore how to use the PERMUTATIONA function as a worksheet function in Microsoft Excel:

We wish to calculate the number of permutations (with repetitions) of six objects, selected from different sized sets.

Syntax:  =PERMUTATIONA(A2,B2)

Result: 9

As you can see above, the function truncates the decimal value to integers, so we got the same result for:

PERMUTATIONA(6,6) and PERMUTATIONA(6,6.5), that is 46656 possible permutations.

Combinations and permutations are different and, hence, they use different formulas. In a combination, the objects can be in any order, whereas in a permutation, the order is important.

Based on the Excel spreadsheet above, the following PERMUTATIONA examples would return:

Note:

1. #VALUE! error – Occurs when “number” or “number_chosen” is not numeric.
2. #NUM! error – Occurs when:
   1. The supplied number argument less than 0; or
   2. The supplied number_chosen argument is less than 0; or
   3. The supplied number argument is less than the number_chosen argument.
3. Difference between PERMUT and PERMUTATIONA Functions
   Both the PERMUT and PERMUTATIONA functions calculate the number of permutations of a selection of objects from a set.However, there is a difference between the two functions. PERMUT does not count repetitions whereas PERMUTATIONA counts repetitions.