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PERMUTATIONA Function (LibreOffice Calc)

Math Intermediate LibreOffice Calc Introduction not established

The PERMUTATIONA function in LibreOffice Calc returns the number of permutations with repetition allowed. It is essential for probability, combinatorics, and counting ordered arrangements where items may repeat.

Verification status: Consult the documentation, examples and any stated test scope below. How formula examples are checked

Availability and version history

  • Introduced: Documented by LibreOffice 26.8.1.1; original introduction not established.
  • Availability: Supported in LibreOffice 26.8.1.1, verified against its function registry. This identifies a supported release, not a final working version.
  • Scope: Desktop Calc, using the English function name. Availability in other spreadsheet applications is separate.
  • Checked: 2026-10-14 — function reference; versioned support. Documentation/source check; not a new native test. Existing example-specific test claims below retain their stated scope.
The **PERMUTATIONA** function returns the number of permutations **with repetition allowed** in LibreOffice Calc. It answers the question: “How many ordered arrangements of length k can be formed from n items if items may repeat?” PERMUTATIONA is essential in probability, combinatorics, code generation, and counting problems involving repeated selections.

What the PERMUTATIONA Function Does

  • Computes permutations with repetition
  • Order does matter
  • Uses the formula:
    n^k
  • Useful for probability, arrangements, and code generation
  • Works with non-integer inputs (truncated)

It is designed to be precise, efficient, and universally compatible.

Syntax

PERMUTATIONA(number; number_chosen)

Arguments

  • number:
    Total number of items (n).

  • number_chosen:
    Number of items to arrange (k), with repetition allowed.

Both arguments must be non‑negative integers (or values that can be truncated to integers).

Basic Examples

Permute 3 items from 5 types (with repetition)

=PERMUTATIONA(5; 3)

Returns 125 (because 5³ = 125).

Permute 2 items from 10 types (with repetition)

=PERMUTATIONA(10; 2)

Returns 100.

PERMUTATIONA with non-integer input

=PERMUTATIONA(6.9; 2.1)

Equivalent to PERMUTATIONA(6; 2) → returns 36.

PERMUTATIONA with cell references

=PERMUTATIONA(A1; B1)

Computes permutations with repetition using values in A1 and B1.

Advanced Examples

Number of possible PIN codes (digits may repeat)

=PERMUTATIONA(10; 4)

Returns 10,000.

Number of possible passwords (letters may repeat)

=PERMUTATIONA(26; A1)

Where A1 is password length.

Number of outcomes when rolling dice (ordered)

=PERMUTATIONA(6; A1)

Equivalent to 6^A1.

Manual formula using POWER

=POWER(A1; B1)

Equivalent to PERMUTATIONA(A1; B1).

Relationship to PERMUT

=PERMUTATIONA(n; k) >= PERMUT(n; k)

Always true because repetition increases possibilities.

PERMUTATIONA for sampling with replacement

=PERMUTATIONA(A1; B1)

Counts ordered samples where items may repeat.

PERMUTATIONA for Cartesian products

=PERMUTATIONA(n; k)

Equivalent to the size of an n × n × … × n (k times) grid.

Common Errors and Fixes

Err:502 — Invalid argument

Occurs when:

  • number < 0
  • number_chosen < 0
  • arguments are text
  • arguments cannot be coerced to integers

Err:503 — Overflow

Occurs when:

  • n^k exceeds Calc’s numeric limit
  • inputs are too large (e.g., PERMUTATIONA(1000; 1000))

PERMUTATIONA returns unexpected results

Cause:

  • Non-integer values are truncated
    Example: PERMUTATIONA(5.8; 2.9) → PERMUTATIONA(5; 2) → 25.

Best Practices

  • Use PERMUTATIONA when order matters and repetition is allowed
  • Use PERMUT when repetition is not allowed
  • Use COMBIN and COMBINA when order does not matter
  • Avoid large inputs (n^k grows extremely fast)
  • Use POWER for manual permutations with repetition
PERMUTATIONA is essential for counting ordered arrangements with repetition — perfect for passwords, codes, dice outcomes, and sampling with replacement.
  • Use PERMUT for permutations without repetition
  • Use COMBIN for combinations without repetition
  • Use COMBINA for combinations with repetition
  • Use FACT and FACTDOUBLE for factorial-based formulas
  • Use POWER(n; k) for manual permutations with repetition

By mastering PERMUTATIONA and its related combinatorics functions, you can build powerful probability, counting, and statistical models in LibreOffice Calc.