COMBIN in Zoho Sheet: Count Unique Teams and Selections

=COMBIN(n; k)

Zoho’s official COMBIN reference uses semicolon-separated inputs. It supplies =COMBIN(11;2) → 55, =COMBIN(24;6) → 134596, and =COMBIN(12;12) → 1. The article describes n as greater than k, even though its own equal-argument example succeeds. For practical whole-number cases, 0 ≤ k ≤ n is the mathematical domain. The exact handling of zero, fractions and text is not exhaustively documented by Zoho and must be tested before relying on such edge cases.

The mathematical rule is n! / (k! × (n−k)!), where ! denotes factorial. If eight candidates are available and three are selected, the arithmetic is 8×7×6 / (3×2×1) = 56. You do not need to enter factorials into the sheet when COMBIN is available. Using COMBIN directly usually makes the model easier to read.

Enter the B/C data below as numeric values in a fresh practice workbook. Enter the formula in G2 and fill down to G9. Expected results come from independent Python integer calculations, not native Zoho Sheet execution.

Step 1: Put the imported column labels in row 1 and preserve row numbers exactly; otherwise formulas in the table will point at different data. Step 2: Click G2 and enter =COMBIN(B2;C2). Step 3: After checking 56, drag the formula down through G9 so the references advance. Step 4: Compare with the independent expected values, review the imported number formats, and confirm your editor accepts the semicolon separator. Step 5: Alter B2 to 9 and predict the new result, COMBIN(9;3)=84, before checking; this tests understanding, not vendor execution.

Suppose an auditor randomly chooses four distinct cartons from a batch of ten, without replacement. Set B4 to 10 and C4 to 4. The possible four-carton samples are =COMBIN(B4;C4) → 210. Now imagine three cartons have defects, seven are acceptable, and the auditor wants exactly two defective and two acceptable cartons in the four-carton selection. Calculate:

=COMBIN(3;2)*COMBIN(7;2)

The expected numerator is 3 × 21 = 63 possible samples meeting that description. The probability of exactly two defective cartons under uniform random selection without replacement is 63/210 → 0.3 (30%). This is a genuine hypergeometric counting example; it is not a prediction that 30% of real-world samples will be defective. The outcome depends on the assumed stock composition and unbiased selection. To model with a spreadsheet, place total options in B4 and sample size in C4, then place the population counts in separately labeled input cells rather than hard-coding them for production.

A common model-building mistake is to divide COMBIN(3;2) by COMBIN(10;4) and forget to count the acceptable cartons. That incorrectly treats different samples that share two defective cartons as a single sample. The second COMBIN term is essential.

Counting logic matters more than a function name. If the same person may not occupy two positions on a panel, choose COMBIN or PERMUT depending on whether positions are ranked. If a flavour can appear more than once in a selection and order does not matter, COMBINA is the mathematically appropriate category; Zoho’s COMBINA reference also documents its own domain restrictions, so do not assume every unusual input is accepted.

Zoho’s checked reference documents semicolon syntax. Microsoft documents Excel COMBIN with number, number_chosen and explicitly says fractional numeric arguments are truncated; this does not prove identical coercion, maximum value or separator rules in Zoho. Locale and current editor settings can affect entry syntax. The official Zoho reference checked 2026-10-11 does not supply a first-supported cloud or mobile version; do not advertise historical or cross-platform parity without native testing. These examples are individually computed using Python’s math.comb, including exact integer arithmetic, not screenshots or executions in Zoho Sheet.