July 2, 2022

# 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:

Syntax: =PERMUTATIONA(A3,B3)
Result: 25

Syntax: =PERMUTATIONA(A4,B4)
Result: 100

Syntax: =PERMUTATIONA(A5,B5)
Result: 16807

Syntax: =PERMUTATIONA(A6,B6)
Result: 512

Syntax: =PERMUTATIONA(A7,B7)
Result: 46656

Syntax: =PERMUTATIONA(A8,B8)
Result: 46656

Syntax: =PERMUTATIONA(A9,B9)
Result: 1000000

Syntax: =PERMUTATIONA(A10,B10)
Result: 13841287201

Syntax: =PERMUTATIONA(A11,B11)
Result: 9

Syntax: =PERMUTATIONA(A12,B12)
Result: 1000

Syntax: =PERMUTATIONA(A13,B13)
Result: 16807

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.
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