PERMUT
Returns the number of permutations (arrangements) of k items from n: n! / (n − k)!. Order matters and items are not repeated.
PERMUT(number, number_chosen)Arguments
numberThe total number of items (must be ≥ 0).number_chosenThe number of items chosen (0 ≤ number_chosen ≤ number).
=PERMUT(5,3)5! / 2! = 60 ordered arrangements of 3 from 5
=PERMUT(10,2)10 × 9 = 90
- •Returns #NUM! if number_chosen > number, or if either argument is negative
- •Use COMBIN() if order does not matter
- •Use PERMUTATIONA() if items can repeat
- •Confusing PERMUT with COMBIN - PERMUT counts arrangements where order matters (like race finish order), while COMBIN counts groupings where order doesn't matter (like committee selection), and PERMUT always returns a result equal to or larger than COMBIN for the same inputs
- •Passing a number_chosen greater than number, which returns a #NUM! error since you can't arrange more items than are actually available
- •Assuming items can repeat in a PERMUT calculation - standard PERMUT assumes each item can only be used once; use PERMUTATIONA if repetition is allowed
COMBINCounts groupings where order doesn't matter, a related but smaller-result counting problem than PERMUT's order-sensitive arrangements.PERMUTATIONACounts permutations that allow repetition, relaxing PERMUT's assumption that each item can only be used once.FACTUsed internally in the mathematical formula behind PERMUT, since permutations are calculated using factorials.What's the difference between PERMUT and COMBIN?
PERMUT counts arrangements where the order matters (like assigning 1st, 2nd, 3rd place), while COMBIN counts groupings where order is irrelevant (like selecting a committee) - PERMUT will always give a result equal to or greater than COMBIN for the same inputs.
Why does PERMUT return a #NUM! error?
You're likely asking to arrange more items (number_chosen) than are actually available (number) - you can't arrange 5 items when you only have 3 to work with.
Does PERMUT allow the same item to be used more than once?
No, standard PERMUT assumes each item is used at most once. Use PERMUTATIONA instead if repetition should be allowed, like counting possible PIN codes where digits can repeat.
Need to translate a formula using PERMUT?
Use our translator to convert your complete formula