Math guide

Combination vs permutation: the practical difference.

The simplest test is this: if changing the order creates a different result, use a permutation. If order does not matter, use a combination.

Combination

Order does not matter

Choosing A and B is the same selection as choosing B and A.

AB, AC, BC
Permutation

Order matters

AB and BA are different because the sequence changes.

AB, BA, AC, CA, BC, CB

Quick decision rule

  • Use combinations for teams, selections, groups, pairs, and unordered sets.
  • Use permutations for rankings, passwords, codes, ordered schedules, and sequences.
  • Use repetition only when the same item can appear more than once inside one result.

Examples

Team of two from Alice, Ben, and Cara

Use a combination. Alice + Ben is the same team as Ben + Alice.

Two-character code from A, B, and C

Use a permutation if AB and BA should count as different codes.

Try both modes

ComboKit Studio includes both a generator and exact count calculators, so you can compare the output size before creating rows.