PERMUTATIONA in Google Sheets: Ordered Choices With Replacement

• Introduced: first service launch date is not established by the official history reviewed; no numbered desktop introduction is assigned.
• Availability: documented in the rolling Google Sheets service. Examples target ordinary web-spreadsheet cells; mobile clients and imported file modes are not separately certified.
• Checked: October 14, 2026; official PERMUTATIONA reference. Documentation and independently calculated examples, without native Sheets execution.

=PERMUTATIONA(number, number_chosen)

Both arguments are required. Google defines the mathematical result as the total pool size raised to the number chosen and documents truncation of both arguments to integers. It also documents #NUM! when number is zero.

Evidence caution: the parameter table says number_chosen must not exceed number, although replacement counting mathematically permits longer sequences. The page’s first result cell also prints 99 for a 3-by-2 example despite its definition and neighboring examples implying nine. This guide uses the mathematical definition for checked counts, stays within the stated parameter restriction, and leaves native number_chosen>number behavior unverified.

Use distinct labels A, B and C:

=PERMUTATIONA(3,2)

Expected count: 9. The complete list is AA, AB, AC, BA, BB, BC, CA, CB, CC. Unlike PERMUT, this model includes AA, BB and CC.

PERMUT without reuse gives six outcomes. Ignoring order while allowing reuse is another question: COMBINA counts the six groups AA, AB, AC, BB, BC and CC. A shared count in two different models does not make their outcome sets identical.

=PERMUTATIONA(3.9,2.8)

The documented truncation rule gives integer inputs three and two, so the expected result is 9. This is not rounding to four and three, whose power would be 64.

Fractional counts rarely represent a sensible pool or sequence length. Prefer explicit whole-number input validation in a real model; the truncation control explains the function’s documented behavior rather than endorsing accidental fractions.

For a pool of five reusable symbols:

All these lengths remain within the parameter table’s stated range. Each new position multiplies the number of sequences by five because reuse keeps every symbol available.

These are combinatorial counts, not estimates of password security or the behavior of a random generator. Restrictions on allowed sequences require their own model.

Use five labels A, B, C, D and E for a three-position sequence. The total is 125. The sequences with no A use only the other four labels, giving 4³=64.

=PERMUTATIONA(5,3)-PERMUTATIONA(4,3)

Expected result: 61 sequences containing at least one A. Both calls satisfy the documented parameter restriction. Subtracting the complement avoids double-counting sequences containing A twice or three times.

Choose which of the three positions holds A, then fill the other two positions from B, C, D and E:

=3*PERMUTATIONA(4,2)

Expected result: 48. The three selected A positions create disjoint cases, and 4²=16 sequences fill the remaining positions in each case.

Exactly one A is a stricter condition than at least one A, so 48 is correctly less than 61. Their difference, 13, counts the sequences with two or three A symbols.

With the same five-symbol pool and three positions, there are five first choices and four choices for each later position:

=5*PERMUTATIONA(4,2)

Expected result: 80. A symbol may reappear in the third position if it differs from the second. The count is therefore different from the no-reuse value PERMUT(5,3)=60 and from the unrestricted replacement count 125.

A zero pool has Google’s documented #NUM! result. Negative counts, an empty sequence, excessive magnitudes and native number_chosen>number behavior are not certified here. Do not remove the stated source conflict merely because the power formula has a mathematical value outside that restriction.

• Google PERMUTATIONA help.
• Editorial testing standards.

Inputs are fictional. Approximate answers are independent mathematical expectations rounded to nine places, not captured native results. Complete type/error matrices, extreme-magnitude accuracy and cross-client behavior remain untested.