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PERMUTATIONA Function

Excel 2007+

Summary

The PERMUTATIONA function calculates the number of permutations possible when selecting a specific number of objects from a larger set, allowing repetitions. Unlike standard permutations, this function accounts for scenarios where the same object can be chosen multiple times in different positions.

Syntax

PERMUTATIONA(number, number_chosen)

Parameters

Parameter	Type	Required	Description
number	`Number`	Yes	The total count of distinct objects available for selection
number_chosen	`Number`	Yes	The size of each permutation (how many positions to fill)

Using the PERMUTATIONA Function

PERMUTATIONA is perfect for scenarios involving arrangements with replacement, such as license plate combinations, password possibilities, or any situation where the same item can occupy multiple positions. The function uses the formula number^number_chosen to compute results efficiently.

Common PERMUTATIONA Examples

3 Objects, Choose 2 (With Repetition)

=PERMUTATIONA(3,2)

For objects [A,B,C], finds all 2-position arrangements allowing repeats: AA, AB, AC, BA, BB, BC, CA, CB, CC (9 total)

2 Items, Full Arrangements

=PERMUTATIONA(2,2)

For items [X,Y]: XX, XY, YX, YY (4 possible arrangements)

Frequently Asked Questions

PERMUTATIONA allows repetitions (replacement), while PERMUTATION does not. PERMUTATIONA uses n^k, PERMUTATION uses n!/(n-k)!.

Arguments are automatically truncated to integers. Use whole numbers for accurate results.

Common Errors and Solutions

#NUM!

Cause: Invalid numeric values (number < 0, or number_chosen > number when number=0)

Solution: Ensure both arguments are non-negative integers

#VALUE!

Cause: Non-numeric arguments provided

Solution: Use only numeric values for both parameters

Notes

Uses formula: number^number_chosen
Both parameters truncated to integers
Maximum safe values depend on Excel's number limits (~10^308)
Available since Excel 2007

Compatibility

Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365

Not available in: Excel 2003, Excel XP, Excel 2000, Excel 97

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+