The Excel PERMUT function returns the number of permutations — the number of ordered arrangements of a given size that can be drawn from a set of objects, where no object is repeated.
Syntax
| Argument | Description | |
|---|---|---|
number | Required | The total number of objects available. Must be greater than or equal to number_chosen. |
number_chosen | Required | How many objects are chosen in each arrangement. Order matters and items are not repeated. |
How to use it
PERMUT counts arrangements where order matters and items are used at most once. It computes n! / (n - k)! — the number of ways to fill k ordered slots from n distinct objects.
Choosing 2 of 5 items in order gives 5×4 = 20 arrangements. If order did not matter you would use COMBIN instead, which would return 10. If items could repeat, use PERMUTATIONA.
Permutation vs combination: PERMUT counts ordered arrangements (AB ≠ BA); COMBIN counts unordered selections (AB = BA). For the same inputs PERMUT is always the larger number.
Try it: interactive demo
Pick a PERMUT example to see the formula and its result.
Practice workbook
Frequently asked questions
What is the difference between PERMUT and COMBIN?
What is the difference between PERMUT and PERMUTATIONA?
PERMUTATIONA allows repetition, so PERMUTATIONA(5,2)=25 (which is 5²) versus PERMUT(5,2)=20.What does PERMUT calculate mathematically?
n! / (n - k)!, where n is the total objects and k is the number chosen. This counts ordered arrangements of k items from n.What happens if number_chosen is bigger than number?
#NUM! error, because you cannot arrange more distinct objects than you have. Both arguments must also be 0 or greater.Master functions like this in one day
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