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.