The Excel PERMUTATIONA function returns the number of permutations with repetition allowed — the count of ordered arrangements of a chosen size when each object may be reused.
Syntax
| Argument | Description | |
|---|---|---|
number | Required | The total number of objects available. |
number_chosen | Required | How many objects are chosen in each arrangement. Order matters and repetition is allowed. |
How to use it
PERMUTATIONA counts ordered arrangements when repetition is allowed. Because every one of the k slots can be filled by any of the n objects, the formula is simply nk.
This is the right count for things like PIN codes, dice rolls, or any scenario where the same value can appear more than once. Compare PERMUT(5,2)=20 (no repeats) with PERMUTATIONA(5,2)=25 (repeats allowed).
Why it equals n to the power k: with repetition, the choice for each slot is independent and there are always n options — so the total is n × n × … (k times), or nk.
Try it: interactive demo
Pick a PERMUTATIONA example to see the formula and its result.
Practice workbook
Frequently asked questions
How is PERMUTATIONA different from PERMUT?
nk; PERMUT forbids repetition, equalling n!/(n-k)!. PERMUTATIONA(5,2)=25 while PERMUT(5,2)=20.Why does PERMUTATIONA equal n to the power of number_chosen?
n × n × … (k times) = nk.Can number_chosen be larger than number in PERMUTATIONA?
number, so =PERMUTATIONA(2,3) is valid and returns 8. Both arguments must still be 0 or greater.When was PERMUTATIONA added to Excel?
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