The Excel PERMUT Function


The number of permutations for a given number of objects is the number of combinations in each possible order.

Note that permutations differ from combinations in that, for a permutation, the order of the objects matters, but in a combination, the order does not matter.

The number of possible permutations is given by the formula:

Permutations Equation

where k is the number of objects chosen and n is the number of possible objects.

For further information, see the Wikipedia Permutation page

Function Description

The Excel Permut function calculates the number of permutations of a specified number of objects from a set of objects.

The syntax of the function is:

PERMUT( number, number_chosen )

Where the function arguments are:

number - The total number of objects available
number_chosen - The number of objects in each permutation (i.e. the number of objects selected from the set)

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

Permut Function Examples

In the following spreadsheet, the Excel Permut function is used to calculate the number of permutations of six objects, selected from different sized sets:

1 =PERMUT( 6, 6 )
2 =PERMUT( 7, 6 )
3 =PERMUT( 10, 6 )
4 =PERMUT( 49, 6 )
1 720
2 5,040
3 151,200
4 10,068,347,520

For further examples of the Excel Permut function, see the Microsoft Office website.

Permut Function Errors

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

Common Errors
#NUM! -

Occurs if either:

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