This article describes the formula syntax and usage of the PERMUTATIONA function in Microsoft Excel.
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, numberchosen)
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:
Remarks

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.
Example
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 
4,4 

4,5 

4,6 

5,4 

5,5 

5,6 

6,4 

6,5 

6,6 

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

3,5 

5,3 

5,5 