PERMUTATIONA Function

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.

A good real-world example is a numeric code: a 3-digit code using the digits 0-9 allows values like 123, 321, and 111. Order matters and digits can repeat, so this is a permutation with repetition. For a full explanation, see Combinations and permutations in Excel.

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.