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Combination vs permutation

Ask two questions in order: does order matter, and can the same item appear more than once?

Decision rule

Start with order

If swapping two chosen items changes the outcome, you are in permutation territory. If swapping them does not change the outcome, you are in combination territory.

Second question

Then check repetition

If the same item can appear more than once, use the repetition version of the formula. If each item can appear only once, use the non-repetition version.

Quick examples

  • Committee from 9 volunteers: combination without repetition.
  • Officer roles from 9 volunteers: permutation without repetition.
  • 3 scoop bowl from 5 flavors, repeats allowed: combination with repetition.
  • 4 character code from 6 symbols, repeats allowed: permutation with repetition.