PERMUTATIONA Function (Gnumeric)

• Introduced: First release not established; present in the retained 1.12.57 source.
• Supported in: Gnumeric 1.12.62; no retirement is established.
• Scope: Desktop Gnumeric with its Statistics plugin. English comma-separated formulas are shown.
• Checked: October 14, 2026. The tables and named advanced check use 1.12.57 ssconvert. Current 1.12.62 source was inspected; that release was not executed.

PERMUTATIONA(n,k) counts ordered sequences of k positions when each position can independently use any of n choices. Repetition is allowed, so the count is n^k. It differs from selecting distinct objects without replacement. Versioned function help.

=PERMUTATIONA(n,k)

n is the number of available choices; k is the number of positions. Both are required and are floored before the nonnegative-domain check.

Current implementation.

The eight ordinary results below were independently checked using integer arithmetic.

A four-digit code using all ten digits, including a leading zero, has =PERMUTATIONA(10,4) = 10000 possibilities. The advanced native check confirms this count. If the first digit cannot be zero, the count changes to 9×10³=9000; the single unrestricted formula no longer describes that rule.

For seven symbols and three positions, the table gives 343. This assumes every position has all seven choices and repeated symbols are permitted. A “no repeated symbol” policy instead needs 7×6×5=210.

The empty sequence gives one outcome, so PERMUTATIONA(n,0)=1, including PERMUTATIONA(0,0)=1. With zero choices and a positive number of positions, the result is zero. This is a counting convention, not a claim about every use of 0^0 in analysis.

Independent concatenation of sequences gives n^(a+b)=n^a×n^b. For n=3, lengths 2 and 3 have 9 and 27 possibilities, and length 5 has 243. Restricting certain neighboring pairs or prescribing quotas would break the independent-choice model and require a different count.

The retained 1.12.57 and 1.12.62 worksheet callbacks have the same relevant argument guards and calculation dispatch. That source comparison does not establish execution or universal floating-point equivalence in the later build.

The help uses the word “truncated,” but the callback floors first. Positive fractions 5.9 and 2.9 become 5 and 2; a negative fraction −0.9 becomes invalid rather than zero. A k larger than n is valid because choices are reused: PERMUTATIONA(2,3)=8.

An empty first cell becomes zero, so the zero-position case can return one despite missing input. Validate that both counts are supplied nonnegative integers when that is the worksheet’s intended contract. Large results are floating-point approximations and can overflow.

F5 is an actually empty cell. Errors below are the tested build’s results, not zero-valued mathematical answers.

• Current worksheet implementation
• Tested-version worksheet implementation

The retained workbook’s stale SUM cache and uncached SUM both recalculated correctly. Formula identities, typed inputs and native results were inspected. The importer reported unsupported style-extension elements; that warning is retained, and no all-formatting claim is made. GUI entry, other locales and later-release output were not tested.

POWER, COMBIN, FACT.