What's the difference between PERMUT and COMBIN?

PERMUT counts ordered arrangements where sequence matters (1st place is different from 2nd place). COMBIN counts unordered selections where sequence does not matter (a team of 3 people is the same regardless of who was picked first). Use PERMUT for rankings, rotations, or schedules; use COMBIN for committees, groups, or combinations.

Why does PERMUT(5, 10) return #NUM!?

You cannot arrange 10 items when only 5 exist. PERMUT requires number_chosen ≤ number. Swap the arguments to =PERMUT(10, 5) (arrange 5 from 10 items) or reduce number_chosen to =PERMUT(5, 2) (arrange 2 from 5 items).

Does PERMUT work with decimal inputs like PERMUT(5.7, 2.3)?

Yes—PERMUT silently truncates decimals to integers, so PERMUT(5.7, 2.3) equals PERMUT(5, 2) and returns 20. For explicit control, wrap arguments in INT() first: =PERMUT(INT(A1), INT(B1)).

What's the largest result PERMUT can return without precision loss?

Results depend on your spreadsheet's floating-point precision. PERMUT(13, 13) = 6,227,020,800 stays within Excel's range, but larger values risk rounding errors. For permutations exceeding PERMUT(20, 10), expect scientific notation or approximation errors.

PERMUT function

Calculates the number of ordered arrangements (permutations) of a subset of items from a larger set, essential for ranking and sequencing tasks.

=PERMUT(number, number_chosen)

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Describe what you need. The generator will reach for PERMUT where PERMUT is the right tool, and tell you when it is not.

Arguments

How PERMUT reads its arguments

Argument	Required	Description
number	Required	The total count of items available; must be non-negative and typically a whole number.
number_chosen	Required	The count of items to arrange in order; must be non-negative and cannot exceed number.

Returns

Returns a whole number representing the count of unique ordered arrangements.

Availability

Excel: All · Google Sheets: Supported

Worked examples

1. Count ranking arrangements for a class award

Student	Math Score
Alice	95
Bob	88
Charlie	91
Diana	94

=PERMUT(4, 3)

Result: 24

The class has 4 students eligible for prizes. To award 1st, 2nd, and 3rd place honors, there are 24 different possible ranking arrangements—because who gets 1st determines which 2 of the remaining 3 can get 2nd and 3rd.

2. Order submitted assignments for grading review

Assignment	Score
HW1	95
Quiz1	88
Essay	91
HW2	89

=PERMUT(4, 2)

Result: 12

A student completed 4 assignments. To select and review exactly 2 of them in a specific sequence (review first, then second), there are 12 possible orderings—because reviewing HW1 then Quiz1 is different from reviewing Quiz1 then HW1.

3. Arrange subjects in a weekly exam schedule

Subject

Math

Science

English

History

Art

=PERMUT(5, 3)

Result: 60

The school offers 5 subjects. To schedule final exams for exactly 3 of them across Monday, Tuesday, and Wednesday, there are 60 possible arrangements—because the order matters: Math-Science-English is a different schedule than Science-Math-English.

Common errors

Which PERMUT error are you seeing?

Error	Why it happens	How to fix it
#NUM!	The number_chosen argument exceeds the number argument—attempting to arrange more items than are available.	Verify that number_chosen ≤ number. For example, change =PERMUT(3, 5) to =PERMUT(5, 3) if you have 5 items but want to arrange only 3 of them.
#NUM!	A negative value was passed for number or number_chosen; permutations cannot be defined for negative set sizes.	Use only non-negative values. If a cell reference might return negative, wrap it with ABS(): =PERMUT(ABS(A1), 2).
#VALUE!	A non-numeric value (text, a date, or a cell containing a name like "Alice") was passed as an argument.	Ensure both arguments reference cells with numbers. If A1 contains a student name, reference a numeric column instead, such as their score or assignment count.

Tips and when to use something else

Use PERMUT when order matters—rankings, sequences, rotations; use COMBIN when order does not matter (teams, committees, groups).
Results grow exponentially with larger inputs: PERMUT(10, 5) = 30,240 and PERMUT(20, 10) exceeds typical spreadsheet integer precision. Watch for scientific notation in large results.
PERMUT truncates decimal arguments to integers, so PERMUT(5.9, 2.1) is treated as PERMUT(5, 2). Use INT() to round explicitly if needed: =PERMUT(INT(A1), INT(B1)).
Combine with IF to validate inputs before calculating: =IF(B1>A1, "Invalid", PERMUT(A1, B1)) prevents #NUM! errors and improves formula reliability.

Related functions

COMBINReturns the number of ways to choose a subset of items from a set when order doesn't matter, useful for sampling strategies and probability calculations.PRODUCTReturns the product of all numeric values supplied as arguments, multiplying them together into a single result.IFThe IF function returns one value if a condition is true and another (or nothing) if it is false, letting you branch logic in a cell.INTINT rounds any number down to the nearest whole integer, always discarding decimal places and rounding toward negative infinity.MATCHMATCH returns the relative position of a lookup value within a one-dimensional range, optionally using exact, less-than, or greater-than matching.

Frequently asked questions

What's the difference between PERMUT and COMBIN?: PERMUT counts ordered arrangements where sequence matters (1st place is different from 2nd place). COMBIN counts unordered selections where sequence does not matter (a team of 3 people is the same regardless of who was picked first). Use PERMUT for rankings, rotations, or schedules; use COMBIN for committees, groups, or combinations.
Why does PERMUT(5, 10) return #NUM!?: You cannot arrange 10 items when only 5 exist. PERMUT requires number_chosen ≤ number. Swap the arguments to =PERMUT(10, 5) (arrange 5 from 10 items) or reduce number_chosen to =PERMUT(5, 2) (arrange 2 from 5 items).
Does PERMUT work with decimal inputs like PERMUT(5.7, 2.3)?: Yes—PERMUT silently truncates decimals to integers, so PERMUT(5.7, 2.3) equals PERMUT(5, 2) and returns 20. For explicit control, wrap arguments in INT() first: =PERMUT(INT(A1), INT(B1)).
What's the largest result PERMUT can return without precision loss?: Results depend on your spreadsheet's floating-point precision. PERMUT(13, 13) = 6,227,020,800 stays within Excel's range, but larger values risk rounding errors. For permutations exceeding PERMUT(20, 10), expect scientific notation or approximation errors.

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Reviewed 2026-09-17