Related Functions:

The PERMUT function returns the number of permutations for a given number of objects that can be selected from number objects.

Syntax

=PERMUT(number,number_chosen)

Arguments

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

Examples

  A B C D
1 Data Description    
2 100 Number of objects    
3 3 Number of objects in each permutation  
4        
5 Formula Result Notes
6 =PERMUT(A2,A3) 970200 Permutations possible for the arguments specified in A2:A3
7 =PERMUT(3,2) 6 Permutations possible for a group of 3 objects where 2 are chosen
8 =PERMUT(6,6) 720 Permutations possible for a group of 6 objects where 6 are chosen

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.

The equation for the number of permutations is:   

    \[    P_{k,n} = \frac{n!}{(n-k)!}    \]

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

See Wikipedia for more information on Permutation