COMBIN in Apple Numbers: Combinations Without Repetition

COMBIN: count unordered selections without replacement. Order does not matter and you may not choose the same item twice. Example: =COMBIN(8,2) has the expected mathematical result 28. Choose a panel, select toppings with no repeats, and count unique groups without regard to order. [A1, M1]

=COMBIN(total-items, group-size)

• total-items (required, number): Number of different available items; must be 0 or greater. Numbers with fractional portions lose their decimals.
• group-size (required, number): Number of distinct items in each selected group; must be 0 or greater. Numbers with fractional portions lose their decimals.

Both arguments are required numeric values; no default value is documented for either. Argument order is significant: first supply the size of the available collection, then the number of items/positions chosen. The function returns a count of outcomes, not a list of the actual outcomes. Apple explicitly documents truncation of fractional parts for both arguments; it does not document a complete matrix of returned error strings. [A1]

How to interpret the count mathematically

For whole numbers, the calculation is n! / (k! × (n-k)!) for whole-number inputs 0 ≤ k ≤ n. This expression is an independent combinatorial identity and provides a convenient check of the expected result. It does not establish undocumented app handling of errors, overflows, large arguments or numeric coercion. [A1, M1]

The English function identifier and syntax above were checked in Apple Formulas and Functions Help 15.4 on 2026-10-12T03:42:00.411513Z. The version 15.4 labels the help edition consulted, not a confirmed minimum release of the Numbers application. Apple’s general guide discusses Numbers on supported Apple devices and web platforms; these four individual articles do not independently certify every historical macOS/iOS/iPadOS/iCloud edition. Translated function names or alternate spellings were not established; none are claimed as aliases. [A1, A2]

Apple’s documented examples use , as the function argument separator. If your decimal separator is a comma, Apple says to use a semicolon between arguments when typing formulas; for example =COMBIN(3;2) instead of =COMBIN(3,2). The formula editor can insert the correct locale punctuation. Function names can be typed in upper or lower case, and parentheses enclose the arguments. [A2]

Cell references follow Numbers conventions: B2 is a same-table cell, and B2:B6 denotes a range. For a cell in another table, Apple documents a qualified reference such as Table 2::B2; for another sheet, Sheet 2::Table 2::B2 is an example. If table names contain spaces, select cells in the formula editor to insert correctly formatted references; do not substitute Excel’s Sheet1!B2 syntax. Below, all formulas use two single numeric cells, not a range argument. [A3]

Verification status: Official Apple documentation checked. Example outcomes independently calculated using Python’s standard-library arithmetic/combinatorics. Not executed in Apple Numbers. Displayed answers are expected, not observed native results. No genuine Apple Numbers screenshots were taken; there are no mock app images in this guide.

Create a Numbers table named SelectionCounts. Place Available in B1, Chosen in C1 and Result in D1. Enter these whole-number inputs into rows 2–6, enter =COMBIN(B2,C2) in D2, and fill the formula down through D6. The expected numbers are independently computed, not observations in Numbers. [A1, A3, M1]

Row: 2

B: Available
3

C: Chosen
2

D formula
=COMBIN(B2,C2)

Expected D
3

Row: 3

B: Available
5

C: Chosen
3

D formula
=COMBIN(B3,C3)

Expected D
10

Row: 4

B: Available
4

C: Chosen
0

D formula
=COMBIN(B4,C4)

Expected D
1

Row: 5

B: Available
8

C: Chosen
2

D formula
=COMBIN(B5,C5)

Expected D
28

Row: 6

B: Available
10

C: Chosen
4

D formula
=COMBIN(B6,C6)

Expected D
210

A reader can also enter these standalone expressions in empty cells to avoid issues caused by table naming or references:

For the first row, use your own labels to enumerate the outcomes and verify the result by hand before trusting it for a larger dataset. Changing B or C changes the count, but the formula does not generate every actual selection. [M1]

Application 1 — teams and panels

Choose a two-person interview panel from eight distinct candidates. There are 28 different panels because swapping the two members produces the same panel. Create a fresh table and place 8 in B2 and 2 in C2; =COMBIN(B2,C2) has expected result 28. This result assumes each item is distinct and cannot be selected twice, and the order inside the group is irrelevant. [A1, M1]

Application 2 — select a distinct set of products

Choose four distinct books from a shelf of ten, without caring about display order. The independently calculated result is 210 distinct four-book groups. Enter 10 in B3 and 4 in C3. =COMBIN(B3,C3) has expected result 210. This is a count of logically possible outcomes under the stated assumptions; real-world constraints such as availability, limited stock, banned sequences or people declining assignments reduce the actually available outcome space. [M1]

Why this is not a permutation

A group containing A and B is the same group as B and A. For three labelled items A, B and C, choosing two produces AB, AC, BC: three results. The six ordered results AB, BA, AC, CA, BC, CB belong instead to PERMUT(3,2). If each possible order counts as an independent outcome, COMBIN undercounts by design. [A1, M1]

Complementary group-size identity

For integer inputs n ≥ 0 and 0 ≤ k ≤ n, a selection of k objects uniquely determines the n−k objects not chosen, so COMBIN(n,k)=COMBIN(n,n-k). For ten items, =COMBIN(10,4) and =COMBIN(10,6) each have the expected answer 210. This is a mathematical identity, not a separate Apple-native execution result. [M1]

When should you use which related function?

Counting question: Choose an unordered unique group

Order significant?
No

Reuse the same item?
No

Function
COMBIN

Counting question: Choose an unordered group with repeats

Order significant?
No

Reuse the same item?
Yes

Function
COMBINA

Counting question: Assign ordered positions with no repeats

Order significant?
Yes

Reuse the same item?
No

Function
PERMUT

Counting question: Build ordered sequences with repeats

Order significant?
Yes

Reuse the same item?
Yes

Function
PERMUTATIONA

The same inputs (3 available items and 2 chosen) produce 3 (COMBIN), 6 (COMBINA), 6 (PERMUT) and 9 (PERMUTATIONA). The two middle results happen to match at 3/2; that does not make the functions interchangeable. Choose based on order and replacement, not solely because a trial output looks plausible. [A1, M1]

Zero items selected, large results and numeric precision

For four available options and zero chosen positions, the expected count is 1: the one empty choice/sequence. Apple’s article for COMBIN does not list this particular zero-group example, so this is a mathematical expectation only. The exercise =COMBIN(4,0) has mathematically expected result 1 and has not been executed in Numbers. [A1, M1]

Combinatorial results can grow extremely quickly with the input size. A calculation may exceed practical displayed precision or spreadsheet numeric limits. For a business decision, validate that your input model and assumptions are reasonable; avoid interpreting a rounded, scientific-notation display as proof of an exact integer stored by the application. No native overflow threshold is asserted here.

Decimal arguments: documented truncation

Apple explicitly drops decimal portions of both numeric arguments for COMBIN. For =COMBIN(5.9,2.1), the truncated arguments are 5 and 2; the expected answer is 10. This expectation follows the documented rule and an independent mathematical calculation, not an observation in the app. If your input values are measurements or statistical estimates, decide explicitly whether truncating them is appropriate instead of silently losing precision. [A1, M1]

For errors, do not infer an exact Numbers error message from this guide. Apple’s individual function entry documents argument constraints but not a comprehensive native error-code matrix. This matters when migrating a workbook from Excel, where a visually similar function may return differently labelled error text. [A1, X1]

Microsoft’s official Excel documentation also lists the function COMBIN and describes the corresponding unordered groups without repetition for current documented Excel editions. The common positive whole-number examples above have the same mathematical interpretation. The argument names differ between Apple’s documentation and Excel’s; cross-file formula conversion, error strings, rounding/coercion details, date/platform availability, separators and references must be checked independently rather than assumed identical. [X1, A1]

Google Sheets, LibreOffice and other apps were not natively tested for this guide. Do not infer that this exact function identifier or its input boundaries exist unchanged in every program. In particular, use Numbers’ ::-qualified cross-table references rather than pasting an Excel Sheet!Cell reference unchanged. [A3]

• [A1] Apple, COMBIN. Formulas and Functions Help, edition 15.4, accessed 2026-10-12T03:42:00.411513Z. Official function article. Supports: exact syntax and argument order, documented numeric constraints and integer coercion, function meaning and explicit Apple examples. The supporting calculation records maps individual claims to article wording and independently computed vectors.
• [A2] Apple, Functions overview, edition 15.4, accessed 2026-10-12T03:42:00.411513Z. Official function syntax and locale rules. Supports: required vs optional arguments, capitalization, parentheses, and semicolon delimiter for decimal-comma locales.
• [A3] Apple, Refer to cells in formulas, edition 15.4, accessed 2026-10-12T03:42:00.411513Z. Official Numbers reference syntax. Supports: cell and range references, double-colon table/sheet qualifications and copy/absolute reference rules.
• [A4] Apple, List of functions by category, edition 15.4, accessed 2026-10-12T03:42:00.411513Z. Official catalogue. Supports canonical English spelling and category; does not certify minimum historical device/release support.
• [X1] Microsoft Support, COMBIN function for Excel, accessed 2026-10-12T03:42:00.411513Z. Official Excel reference. Supports only the Excel-specific comparison and existence claim, not a Numbers error-code claim.
• [M1] Independent mathematical check with Python math.comb / math.perm / integer exponent operations and a manual enumeration for the small case. Input/output vectors and calculation method are preserved in the evidence JSON. This is not native Apple Numbers execution.

• FACT — continue with a related Apple Numbers calculation.
• FACTDOUBLE — continue with a related Apple Numbers calculation.
• COMBINA — continue with a related Apple Numbers calculation.
• PERMUT — continue with a related Apple Numbers calculation.
• PERMUTATIONA — continue with a related Apple Numbers calculation.

For a software-specific comparison: LibreOffice Calc COMBIN, Apache OpenOffice Calc COMBIN, Gnumeric COMBIN. A shared name does not establish identical argument, error or version behaviour.

The linked official function documentation was reviewed on October 12, 2026. Apple’s Formulas and Functions Help 15.4 identifies the documentation edition, not a minimum Numbers release or a guarantee of historical platform parity. Selected worked examples were checked using independent mathematical or text-processing models; results are expected values, not observations from the spreadsheet application. Native Apple Numbers execution was not performed. Undocumented coercion, exact error messages and platform-specific behaviour remain unverified.

View reproducible example inputs and independent check results. This record is not a native spreadsheet test log.