Counting: permutations and combinations · Year 13
In Year 13 you learn: combinations.
Counting techniques find how many ways something can happen without listing every possibility. Multiply the choices at each stage. Use permutations when the order matters and combinations when it does not.
Key facts
- Product rule: m ways for one choice and n ways for the next give m × n ways together.
- There are n! = n × (n − 1) × … × 1 ways to arrange n different items in a line. Also, 0! = 1.
- Permutations (order matters): nPr = (n!)/((n − r)!).
- Combinations (order does not matter): nCr = (n!)/(r!(n − r)!).
- Arrangements with identical items: (n!)/(a! b! …).
- n people round a circular table: (n − 1)! arrangements.
- “At least one” = total − “none”.