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Excel PERMUTATIONA Function

Excel PERMUTATIONA function
Summary 

The Excel PERMUTATIONA function returns the number of permutations (combinations where order is significant) for a given number of items. The PERMUTATIONA function allows repetitions. To calculate the number of permutations without repetitions, use the PERMUT function.

Purpose 
Get number of permutations with repetitions
Return value 
Number of permutations as an integer
Syntax 
=PERMUTATIONA (number, number_chosen)
Arguments 
  • number - The total number of items.
  • number_chosen - The number of items in each combination.
Version 
Usage notes 

The Excel PERMUTATIONA function returns the number of permutations (combinations where order is significant) for a given number of items. The PERMUTATIONA function allows repetitions. To calculate the number of permutations without repetitions, use the PERMUT function.

A permutation is a combination where order matters. In other words, a permutation is an ordered combination. There are two types of permutations:

  1. Permutations where repetition is not allowed (i.e. 123)
  2. Permutations where repetition is allowed (i.e. 333)

The PERMUTATIONA function calculates permutations where repetitions are allowed. To calculate permutations where repetitions are not allowed, use the PERMUT function.

Example

To use PERMUTATIONA, specify the total number of items and "number chosen", which represents the number of items in each combination. For example, to calculate 3-number permutations for the numbers 0-9, there are 10 numbers and 3 chosen, so the formula is:

=PERMUTATIONA(10,3) // returns 1000

You can see this result in cell D8 in the example shown.

Notes

  • A permutation is a group of items in which order/sequence matters.
  • If order is not significant, see the COMBIN function.
  • Arguments that contain decimal values are truncated to integers.
  • PERMUTATIONA returns a #VALUE! error value if either argument is not numeric.

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