Zoho Sheet PERMUTATIONA: Count ordered selections with repetition
Count repeated ordered selections with PERMUTATIONA in Zoho Sheet, distinguish n^k from permutations without replacement and note the documented domain restriction.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =PERMUTATIONA(3;2) has the independent counting result 9: each of two ordered positions can contain any of three choices, and repetition is allowed.
Documented domain caution: Zoho’s error table lists n < k as #NUM!, even though the underlying repeated-choice counting problem can be meaningful when k exceeds n. Keep that software-specific stated restriction separate from the mathematics; this guide does not claim a runtime test resolving it.
Syntax
=PERMUTATIONA(n; k)
n is the number of available objects or choices; k is the number of positions selected. Zoho describes ordered selections with repetitions. Both arguments are required. Its error table lists negative n or k and n less than k as numeric errors. Official PERMUTATIONA reference.
Use nonnegative whole-number inputs, with n at least k for these examples. The article does not specify fractional-argument truncation or all zero-base boundaries, so those are not borrowed from another application’s implementation.
Enumerate a complete small example
Enter 3 in B2 and 2 in B3. In B5 enter =PERMUTATIONA(B2;B3). The independent result is 9.
Label the three choices A, B and C. The complete ordered pairs are:
- AA, AB, AC
- BA, BB, BC
- CA, CB, CC
There are three possibilities for the first position and three for the second, giving 3*3 = 9. AB and BA are different ordered outcomes. AA, BB and CC are allowed because repetition is permitted.
This list supplies a transparent combinatorial check without executing a Zoho workbook. If your intended rules exclude repeated choices or ignore order, the model has changed and this function is not answering the same question.
Compare related counting models
For three choices and two positions:
| Model | Independent count | Reason |
|---|---|---|
| Ordered, repetition allowed | 9 | 3×3 |
| Ordered, no repetition | 6 | 3×2 |
| Unordered, no repetition | 3 | AB, AC, BC |
PERMUT addresses ordered selections without repetition. COMBIN addresses unordered choices without repetition. Similar terminology does not make these functions aliases.
The repeated-choice formula is n^k because each position independently retains all n choices. This is a counting formula, not a probability. A probability calculation also needs a model for how outcomes are selected; equal counts alone do not establish that every outcome is equally likely.
Practical example: labelled configurations
Suppose a demonstration has four available symbols and three labelled positions, with reuse allowed. =PERMUTATIONA(4;3) has the independent result 64, from 4*4*4. The positions might represent three ordered configuration fields; do not collapse the first and third fields just because they can contain the same symbol.
For ten possible digits in each of two positions, =PERMUTATIONA(10;2) gives the counting reference 100, including repeated digits. Leading-zero strings count as distinct two-position sequences in this model. If the first position must be nonzero, the count becomes 9*10 = 90, a different constrained product; the unrestricted function call would overcount.
For five choices in five positions, the repeated-choice reference is 5^5 = 3125, not 5! = 120. Factorial counts a different arrangement problem in which all five distinct items are used once.
Boundary reasoning and precision
With a positive n and k=0, the independent combinatorial count is 1, the empty selection. Thus =PERMUTATIONA(10;0) has reference value 1. With n=k=1, the count is also 1. The undefined or convention-dependent 0^0 corner is not asserted here.
Negative arguments are outside the documented domain. Large powers grow rapidly, so a displayed scientific-notation result can represent a very large count without showing every digit. The article does not establish an exact-integer range or overflow threshold; use small counts when independently checking precision.
For example, the mathematical repeated-choice problem n=2,k=3 has eight outcomes, but Zoho’s listed n<k error condition prevents treating =PERMUTATIONA(2;3) as a supported result here. This distinction is important when translating an abstract counting problem into a particular spreadsheet function.
Availability and evidence scope
The official rolling article was recovered and checked October 18, 2026. All worked counts are independently enumerated or calculated; no authored Zoho execution was performed. The sources do not establish introduction version, mobile parity or historical lifecycle. The documented domain caveat remains visible rather than being silently replaced by another product’s behavior.