# The Excel PERMUTATIONA Function

Combinations & Permutations
Note that combinations differ from permutations in that in a combination the objects can be in any order, but in a permutation, the order is important.
Permut and Permutationa Functions

The Excel Permut and Permutationa functions both calculate the number of permutations of a selection of objects from a set.

However, the two functions differ in that the Permut function does not count repetitions whereas the Permutationa function does count repetitions.

For example, in a set of 3 objects, a, b, c, how many permutations of 2 objects are there?

• The Permut Function returns the result 6 (permutations: ab, ac, ba, bc, ca, cb);
• The Permutationa function returns the result 9 (permutations: aa, ab, ac, ba, bb, bc, ca, cb, cc).

## Function Description

The Excel Permutationa function calculates the number of permutations, with repetitions, of a specified number of objects from a set.

The syntax of the function is:

PERMUTATIONA( number, number_chosen )

Where the function arguments are:

 number - The total number of objects in the set (must be ≥ 0). number_chosen - The number of objects selected from the set (must be ≥ 0).

Note that, if any of the arguments are supplied as decimal values, they are truncated to integers by the permutationa function.

## Permutationa Function Examples

In the spreadsheet below, the Excel Permutationa function is used to calculate the number of permutations (with repetitions) of six objects, selected from different sized sets.

Formulas:
A
1=PERMUTATIONA( 6, 6 )
2=PERMUTATIONA( 7, 6 )
3=PERMUTATIONA( 10, 6 )
4=PERMUTATIONA( 49, 6 )
Results:
A
146,656
2117,649
31,000,000
413,841,287,201

For further details and examples of the Excel Permutationa function, see the Microsoft Office website.

## Permutationa Function Errors

If you get an error from the Excel Permutationa Function, this is likely to be one of the following:

Common Errors
 #NUM! - Occurs if either:The supplied number argument is < 0;The supplied number_chosen argument is < 0;The supplied number argument is < the number_chosen argument. #VALUE! - Occurs one or both of the supplied arguments are non-numeric.