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| Problem | Excel function | Example | Result |
|---|---|---|---|
| Order does not matter; no repetition | COMBIN |
=COMBIN(8,2) |
28 |
| Order does not matter; repetition allowed | COMBINA |
=COMBINA(4,3) |
20 |
| Order matters; no repetition | PERMUT |
=PERMUT(3,2) |
6 |
| Order matters; repetition allowed | PERMUTATIONA |
=PERMUTATIONA(3,2) |
9 |
These functions are listed by Microsoft for Microsoft 365, Excel for the web, Excel 2024, Excel 2021, Excel 2019, and Excel 2016, although behavior and availability can vary by build or platform. See Microsoft’s Excel function reference.
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Combinations vs. permutations: the decision rule
A combination counts selections where internal order is irrelevant. Choosing Alice and Bob for a two-person team is the same group as choosing Bob and Alice.
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1Fix the driver behind crashes, sound loss and screen glitches2Clear out junk files and repair common Windows errors3Scan for outdated or missing drivers - takes under a minuteA permutation counts ordered selections or arrangements. Assigning Alice to first place and Bob to second is different from assigning Bob to first and Alice to second.
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Next ask whether a choice can be reused:
| No repetition | Repetition allowed | |
|---|---|---|
| Order does not matter | COMBIN |
COMBINA |
| Order matters | PERMUT |
PERMUTATIONA |
“Repetition allowed” means that the same choice may be selected again during the calculation. It does not automatically mean that duplicate labels in a worksheet list are distinct objects.
Calculate combinations with COMBIN
Use COMBIN when you choose k items from n available items, order does not matter, and an item cannot be selected twice.
=COMBIN(number, number_chosen)For example:
=COMBIN(8,2)The result is 28: there are 28 distinct two-person groups from eight people.
For a reusable worksheet, place the total number of items in A2 and the number selected in B2:
| Cell | Value |
|---|---|
A2 |
8 |
B2 |
2 |
C2 |
=COMBIN(A2,B2) |
Microsoft documents the underlying formula as:
n! / (k! × (n-k)!)
See Microsoft’s COMBIN documentation.
Calculate combinations with repetition using COMBINA
Use COMBINA when order does not matter but a category or item may be selected more than once. For example, choosing three scoops from four ice-cream flavors allows vanilla, vanilla, and chocolate.
=COMBINA(number, number_chosen)=COMBINA(4,3)The result is 20. The mathematical formula is:
(n+k-1)! / (k! × (n-1)!)
With cell references, use =COMBINA(A2,B2). This is not the same as COMBIN(A2,B2): the latter treats each available item as usable only once. Read Microsoft’s COMBINA documentation.
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Calculate permutations with PERMUT
Use PERMUT when order matters and each item can be used only once. Typical examples include assigning gold, silver, and bronze positions or filling ranked positions from a group of candidates.
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=PERMUT(number, number_chosen)=PERMUT(3,2)The result is 6. For a larger example, =PERMUT(100,3) returns 970,200.
The formula is:
n! / (n-k)!
If A2 contains 10 and B2 contains 3, =PERMUT(A2,B2) returns 720. See Microsoft’s PERMUT documentation.
Calculate permutations with repetition using PERMUTATIONA
Use PERMUTATIONA when order matters and each position can reuse any of the available choices. This is the model for many PIN, password, or symbol-slot calculations when reuse is permitted.
=PERMUTATIONA(number, number_chosen)=PERMUTATIONA(3,2)The result is 9. With symbols A, B, and C in two ordered positions, the outcomes are:
AA, AB, AC, BA, BB, BC, CA, CB, CC
The mathematical formula is n^k. Thus, =PERMUTATIONA(10,3) returns 1,000. Microsoft’s reference for this function is available at PERMUTATIONA.
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Use FACT for factorials and full arrangements
A factorial multiplies every positive integer from a number down to 1:
n! = 1 × 2 × 3 × ... × n
Excel calculates it with:
=FACT(number)=FACT(5)The result is 120. Excel also defines zero factorial as one, so =FACT(0) returns 1. See Microsoft’s FACT documentation.
To arrange all six distinct items, use:
=FACT(6)The result is 720, equivalent to =PERMUT(6,6). This is different from arranging only some of the items.
Manual combination and permutation formulas
Factorials are useful for learning the mathematics or auditing a worksheet, although the named functions make the spreadsheet’s intent clearer.
Manual combination formula:
=FACT(n)/(FACT(k)*FACT(n-k))For eight items and two selected:
=FACT(8)/(FACT(2)*FACT(6))This returns 28.
Manual permutation formula:
=FACT(n)/FACT(n-k)For three items arranged in two positions:
=FACT(3)/FACT(1)This returns 6. In production workbooks, prefer COMBIN and PERMUT where possible because they communicate the calculation directly and reduce the chance of mistyping a factorial expression.
Important input rules and error messages
#NUM!
#NUM! generally means that the numeric arguments violate the particular function’s constraints. Common causes include negative values or choosing more items than are available.
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For COMBIN, Microsoft specifies invalid results when number or number_chosen is negative, or when number is less than number_chosen. PERMUT also requires a positive number. The repetition functions have their own constraints, so check the relevant Microsoft page rather than applying one rule to every function.
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A basic validation wrapper for COMBIN is:
=IF(OR(A2<0,B2<0,A2<B2),"Check inputs",COMBIN(A2,B2))For PERMUT, also reject a zero total:
=IF(OR(A2<=0,B2<0,A2<B2),"Check inputs",PERMUT(A2,B2))For edge cases involving zero selections or zero available choices, test the exact function and arguments in the Excel version you use.
#VALUE!
#VALUE! usually indicates that one or both arguments are not numeric. Check for headers included in a reference, numbers stored as text, words such as “eight,” hidden spaces, or imported values that contain unexpected characters.
If the cells contain numeric text that Excel can convert, try:
=COMBIN(VALUE(A2),VALUE(B2))VALUE will not repair arbitrary words or malformed imported data. To validate first:
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One free scan finds every outdated or missing driver and matches the right update for your exact hardware.Free scan · exact hardware match=IF(AND(ISNUMBER(A2),ISNUMBER(B2)),COMBIN(A2,B2),"Enter numbers")Decimal arguments
Microsoft documents these functions as truncating non-integer arguments rather than rounding them. For example, COMBIN(8.9,2.9) is treated as though the arguments were 8 and 2. If decimals should be rejected, validate them explicitly:
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=IF(OR(A2<>INT(A2),B2<>INT(B2)),"Use whole numbers",COMBIN(A2,B2))Also confirm that the values are nonnegative and that the chosen quantity does not exceed the available quantity.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Do not confuse repetition with duplicate values
COMBINA and PERMUTATIONA model the reuse of choices. They do not automatically count unique arrangements of a list containing duplicate values.
For the letters in AAB, PERMUTATIONA(2,3) would model three positions filled from two choices with reuse allowed. That is not the same question as finding unique arrangements of the specific multiset AAB.
The unique arrangements of AAB are AAB, ABA, and BAA. The standard multiset formula is:
n! / (m1! × m2! × ... × mr!)
For AAB:
=FACT(3)/FACT(2)This returns 3. If your worksheet contains duplicate records, decide whether duplicates represent repeatable categories, separate physical items, or identical values that should be counted only once. The correct model depends on that distinction.
Using the results in probability calculations
These functions return counts, not probabilities. A probability normally requires:
favorable outcomes / total outcomes
For example, a lottery calculation might use COMBIN to count the total number of unordered ticket combinations, then divide a favorable count by that total:
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=favorable_count/COMBIN(total_numbers,numbers_chosen)The appropriate function depends on the lottery’s actual rules: whether order matters, whether numbers can repeat, and whether every outcome is equally likely. Do not use a combination result as a probability without forming the relevant ratio.
Quick reference
| Situation | Formula | Example result |
|---|---|---|
| Select 2 from 8; order irrelevant | =COMBIN(8,2) |
28 |
| Select 3 from 4 types; repetition allowed | =COMBINA(4,3) |
20 |
| Arrange 2 positions from 3; no reuse | =PERMUT(3,2) |
6 |
| Fill 2 ordered slots from 3 symbols; reuse allowed | =PERMUTATIONA(3,2) |
9 |
| Arrange all 5 distinct objects | =FACT(5) |
120 |
| Select 3 from 10; order irrelevant | =COMBIN(10,3) |
120 |
| Arrange 3 from 10 | =PERMUT(10,3) |
720 |
| Choose 3 from 10 with repetition | =COMBINA(10,3) |
220 |
| Arrange 3 positions from 10 with repetition | =PERMUTATIONA(10,3) |
1,000 |
For most spreadsheet calculations, identify order first, then repetition. Enter the total number available as the first argument and the number chosen as the second, and validate the inputs before relying on the result.
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