Counting / Permutations And Combinations
Least You Need to Know: Permutations and Combinations
Use a **permutation** when order matters. Use a **combination** when order does not matter.
The least you need to know
- Order matters for arrangements, rankings, and codes.
- Order does not matter for committees or chosen sets.
- nPr counts ordered selections.
- nCr counts unordered selections.
- A common check is to ask whether swapping two chosen objects changes the outcome.
Key notation
nPr
permutations of r from n
nCr
combinations of r from n
!
factorial
Tiny worked example
- Choosing 3 students for a committee from 10 uses combinations because the same 3 students form the same committee in any order.\n- Choosing president, vice-president, and secretary from 10 uses permutations because the roles matter.
Common mistakes
- Students often use permutations when choosing a set.
- Students often use combinations when assigning roles.
- Students often forget that repeated orderings can describe the same committee.
How to recognize this kind of problem
- Words like arrange, rank, and code usually mean order matters.
- Words like choose, select, and committee often mean order does not matter.
- Ask whether switching two chosen objects creates a different result.