COMBIN in Excel: Count Unordered Selections Without Replacement

• Introduced: First introduction version is not established by the official history reviewed.
• 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 COMBIN reference. Documentation and independently calculated examples; no native Excel execution or broader platform certification.

=COMBIN(number,number_chosen)

Both arguments are required: the number of available objects and the number selected. Microsoft truncates numeric noninteger arguments. It documents #VALUE! for nonnumeric input and #NUM! for a negative count or a selected count greater than the available count.

Use nonnegative whole counts when constructing a real selection model. The documented truncation of a decimal input is not evidence that a fractional person, card or component makes sense in that model. Examples use English names and comma separators.

From four distinct labels A, B, C and D, the two-label groups are AB, AC, AD, BC, BD and CD.

=COMBIN(4,2)

Expected result: 6, matching the complete list. AA is excluded because there is no replacement. BA is not added because order is ignored. This short enumeration is a useful control for the meaning of the function, beyond checking arithmetic alone.

Put selected counts 0, 1, 2, 3, 4, 5, 6 in A2:A8. With six available labels, fill =COMBIN(6,A2) down.

Expected counts are 1, 6, 15, 20, 15, 6, 1. Selecting none gives one empty set; selecting all six gives one complete set. Choosing k objects is equivalent to choosing the 6−k omitted objects, which explains the symmetric table.

The positive truncation control =COMBIN(6.8,2.9) has expected result 15, because the documented integer arguments become 6 and 2.

Choose three cards from seven distinct cards:

=COMBIN(7,3)

Expected unordered count: 35. If those same three cards instead occupy first, second and third labeled slots, each group has FACT(3)=6 orders. The ordered count becomes 210.

A title such as choose three can hide this distinction. State whether the output is a set of cards or an assignment to three different positions. FACT helps expose the ordering factor at small sizes.

Among six available objects, mark one special. A two-object subset either includes it or excludes it. The included case selects one companion from the other five; the excluded case selects both from those five:

=COMBIN(5,1)+COMBIN(5,2)

Expected result: 15, from 5+10, agreeing with COMBIN(6,2). These cases are disjoint and cover every valid pair, so the addition is justified. Adding overlapping cases would double-count outcomes.

Choosing two units from three repeatable types permits AA, BB and CC as well as AB, AC and BC. That has six outcomes rather than COMBIN(3,2)=3. COMBINA addresses combinations with repetition within its documented scope.

For explicit whole-count controls, COMBIN(3,4) and COMBIN(−1,1) have documented #NUM! expectations. Do not convert these invalid selection rules into a zero count without deciding what the report should mean.

The factorial identity n!/[k!(n−k)!] explains the mathematics but may create much larger intermediate values than the final count. This guide does not establish native exactness or overflow behavior for every large combinatorial input.

• Microsoft COMBIN 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.