Related Functions:

The PERMUTATIONA function returns the number of permutations for a given number of objects, with repetitions, that can be selected from the total objects.

  • This function was introduced in Excel 2013 and so is not available in earlier versions.

Syntax

=PERMUTATIONA(number,number_chosen)

Arguments

Argument Description
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: If any of the arguments are input as decimal values, they will be truncated to integers.

Examples

  A B C
1 Formula Result Notes
2 =PERMUTATIONA(6,6) 46,656 There are 45,656 ways 6 objects can be arranged in groups of 6 with repetition
3 =PERMUTATIONA(10,6) 1,000,000  

Common Function Error(s)

Problem What went wrong
#VALUE! Occurs if either the number or the number_chosen argument is non-numeric
#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

A permutation is any set or subset of objects or events where internal order is significant. Permutations are different from combinations in that, for a permutation, the order of the objects matters, but in a combination, the order does not matter.

PERMUTATIONA uses the following equation:  

    \[   PERMUTATIONA=Total^{Chosen}    \]

See Wikipedia for more information on Permutation