COMBIN in Google Sheets: Unordered Groups Without 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 use ordinary web-spreadsheet numeric cells; other clients and imported files are not separately certified.
• Checked: October 14, 2026; official COMBIN reference. Documentation and independent calculations, without native Sheets execution.

=COMBIN(n,k)

The first argument is the available pool size; the second is the number chosen. Google identifies this as the standard n-choose-k operation and supplies the factorial-ratio identity FACT(n)/(FACT(k)*FACT(n-k)).

These examples use whole counts with 0≤k≤n. The dedicated Google page does not state every fractional-input conversion or exact native domain error. Do not assume that another application’s truncation and error rules have been established for Sheets by this definition alone.

Choose two labels from A, B and C:

=COMBIN(3,2)

Expected count: 3, from AB, AC and BC. AA is not allowed because the same object is not reused. BA does not add an outcome because order is ignored.

If the same three labels instead fill first and second positions, there are six ordered assignments. If labels may repeat but order still does not matter, AA, BB and CC add three outcomes. Each variant needs a different counting rule.

Put selected counts 0 through 7 in A2:A9. With seven available labels, fill =COMBIN(7,A2) down.

Expected mathematical outputs are 1, 7, 21, 35, 35, 21, 7, 1. Choosing nothing gives one empty subset, and choosing all seven gives one complete subset. Those endpoints follow the standard combinatorial model; no new native boundary run was performed.

The table is symmetric because choosing k labels is equivalent to choosing which 7−k labels are left out. This gives an independent consistency check without sorting any actual records in the sheet.

Eight distinct cards are available and three are selected:

=COMBIN(8,3)

Expected unordered count: 56. If the three selected cards fill three labeled positions, each group has FACT(3)=6 orders, producing 336 assignments.

Use FACT to see that ordering factor explicitly in small examples. A column labeled combinations should not contain an ordered-assignment count merely because both are whole numbers.

Mark one of seven available labels. A two-label group either contains it or does not. The first category selects one companion from six; the second selects both labels from those six:

=COMBIN(6,1)+COMBIN(6,2)

Expected total: 21, from 6+15, agreeing with COMBIN(7,2). The two cases are disjoint and exhaustive. Adding overlapping cases would count some outcomes twice.

For a two-unit choice from three repeatable types, COMBINA gives 6 instead of three. The repeatable types describe a different population from three individually limited objects.

For n=8 and k=3, the documented factorial ratio gives 40320/(6×120)=56. It explains the mathematics but can create large intermediate numbers for bigger arguments; do not interpret equivalence as a blanket native overflow guarantee.

Validate nonnegative whole counts and the selected count’s relationship to the available pool. An invalid request should receive a policy-driven explanation rather than a guessed native error code or an invented zero count. Text conversions, extreme magnitudes and cross-client behavior remain outside these finite checks.

• Google COMBIN help.
• Editorial testing standards.

Inputs are fictional. Approximate numerical answers are independently calculated mathematical expectations rounded to nine places, not captured native results. Complete coercion, extreme-magnitude and cross-client behavior remain untested.