Math
FACT function: calculate factorials, route permutations, and combinations
Compute n! arrangements, ordered permutations n! / (n - k)!, and unordered combinations using FACT.
Count delivery route orders and team combinations
FACT(number) returns n! = 1 * 2 * ... * n (truncating any decimal input to an integer first). Five delivery stops can be sequenced in FACT(5) = 120 distinct orders.
To pick k = 3 ordered podium spots from n = 6 finalists, compute FACT(6) / FACT(6 - 3) = 720 / 6 = 120 permutations. Dividing further by FACT(3) gives 20 unordered 3-person committees.
For these counting formulas use integers with 0 <= k <= n. Factorials grow quickly; these small examples do not demonstrate safe calculation for arbitrarily large inputs.
| PoolSize n (A) | PickCount k (B) | Full n! | Ordered P(n,k) | Unordered C(n,k) |
|---|---|---|---|---|
| 6 | 3 | 720 | 120 | 20 |
Zero factorial equals 1; negative inputs return #NUM!
By mathematical definition FACT(0) = 1—which keeps FACT(n) / FACT(n - n) valid when k = n. Negative integer inputs return #NUM!. Validate nonnegative input before relying on truncation: Arte Sheets truncates before its sign check.
=FACT(A2) / FACT(A2 - B2)Unordered combinations formula
Dividing P(n, k) by FACT(k) removes duplicate orderings of the same selected items.
=FACT(A2) / (FACT(B2) * FACT(A2 - B2))Try the example
Use the original values or change them to test your understanding.