PERMUT Function

Excel Functions › Statistical

All versions Statistical

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.


Quick answer:
=PERMUT(5,2) ordered pairs from 5 items = 20

Syntax

=PERMUT(number, number_chosen)
ArgumentDescription
numberRequiredThe total number of objects available. Must be greater than or equal to number_chosen.
number_chosenRequiredHow 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.

=PERMUT(5,2) // = 20
=PERMUT(10,3) // = 720

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.

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Result:

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Frequently asked questions

What is the difference between PERMUT and COMBIN?
PERMUT counts arrangements where order matters (AB is different from BA); COMBIN counts selections where order does not matter (AB is the same as BA). PERMUT(5,2)=20 while COMBIN(5,2)=10.
What is the difference between PERMUT and PERMUTATIONA?
PERMUT forbids repetition — each object is used at most once. PERMUTATIONA allows repetition, so PERMUTATIONA(5,2)=25 (which is 5²) versus PERMUT(5,2)=20.
What does PERMUT calculate mathematically?
It computes 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?
PERMUT returns the #NUM! error, because you cannot arrange more distinct objects than you have. Both arguments must also be 0 or greater.

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Related functions: PERMUTATIONA · COMBIN · COMBINA · FACT · MULTINOMIAL