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**:

- #VALUE! error – Occurs when “number” or “number_chosen” is not numeric.
- #NUM! error – Occurs when:
- The supplied number argument less than 0; or
- The supplied number_chosen argument is less than 0; or
- The supplied number argument is less than the number_chosen argument.

- 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.