PERMUTATIONA in Excel: Count Ordered Choices with Repetition

• Introduced: Microsoft marks the function as introduced in Excel 2013. Version-marker reference.
• Availability: official help lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Checked: October 14, 2026; official PERMUTATIONA reference. Documentation and independently calculated examples; no native Excel execution or broader platform certification.

=PERMUTATIONA(number, number_chosen)

Both arguments are required. Microsoft truncates them to integers and documents #VALUE! for nonnumeric types. It gives zero available objects with a positive chosen count as an invalid numeric case producing #NUM!.

The worked models use positive available counts and nonnegative whole-number position counts. The specific zero-available/zero-chosen convention and a complete negative-input matrix are not established here. The function counts outcomes; it does not generate their labels in cells.

For labels A, B and C and two ordered positions, the possibilities are:

=PERMUTATIONA(3,2)

Expected result: 9. AA, BB and CC are valid because labels may be reused. AB and BA are separate because order matters.

Without reuse, PERMUT gives six. If repetition is allowed but order is ignored, COMBINA represents a different six-outcome model for this particular small case. Equal totals do not mean the selected outcome sets are equivalent.

Three labels and four positions have 3×3×3×3=81 outcomes. Unlike a no-reuse model, the position count can exceed the number of labels.

For an available count of three and position counts 1, 2, 3, 4, 5, expected results are 3, 9, 27, 81 and 243. Each added position multiplies the count by three rather than adding three.

For the documented truncation control, =PERMUTATIONA(3.9,2.8) has expected result 9, using three and two. Validate integer business inputs rather than silently relying on truncation to repair them.

The three-position strings AAB, ABA and BAA use exactly two A labels and one B label, giving three outcomes. A formula =PERMUTATIONA(2,3) instead gives eight, because it allows AAA, ABB, BBB and other label-count patterns too.

For prescribed counts two and one, MULTINOMIAL or =FACT(3)/(FACT(2)*FACT(1)) gives the expected three. The repeated-choice function does not enforce fixed totals of each label.

This distinction matters for worksheet models of category sequences: independent per-position choices and rearrangements of an existing collection are different populations.

Among all three-position strings using A, B or C, the unrestricted count is 27. Strings with no A use only B and C, giving 8. Therefore the number containing at least one A is:

=PERMUTATIONA(3,3)-PERMUTATIONA(2,3)

Expected result: 19. Subtracting the excluded set avoids accidentally counting strings with multiple A labels more than once.

For comparison, strings with exactly one A have three choices for its position and two choices in each remaining position: 3×2²=12. At least one and exactly one are different constraints and should be written explicitly in the model.

With three available labels and four positions, impose an extra rule that neighboring positions must differ. There are three choices for the first position and two choices at each later position, giving 3×2³=24.

That is smaller than the unrestricted PERMUTATIONA count 81. The function itself has no adjacency argument; this constraint requires a separately derived model rather than an extra undocumented parameter.

For a positive available count and zero positions, the mathematical empty-sequence expectation is one. The guide does not turn that statement into a claim about the ambiguous zero-available/zero-position native boundary.

=PERMUTATIONA(0,2) falls under Microsoft’s explicit #NUM! example condition. Large powers can also exceed practical numeric precision, so these finite enumerations do not certify every magnitude. Keep order, reuse and additional constraints visible alongside the formula.

• Microsoft PERMUTATIONA reference.
• Editorial testing standards.

Worked inputs are fictional. Decimal answers are independently calculated mathematical expectations rounded to nine places, not captured native results. Extreme magnitudes, complete coercion matrices and cross-version numerical accuracy remain untested.