Systematic listing
- List outcomes in a logical order so you don't miss any or repeat any.
- Fix the first item and change the others, then move to the next first item: for a coin and a spinner numbered 1 to 3: H1, H2, H3, T1, T2, T3.
The product rule
- If there are m ways of doing one thing and n ways of doing another, there are m × n ways of doing both.
- 3 starters and 4 main courses give 3 × 4 = 12 different meals.
- It works for more than two choices: 4 tops, 3 pairs of trousers and 2 pairs of shoes give 24 outfits.
With and without repeats
- If items can be repeated, each position has the same number of choices: 4-digit PINs from 0–9 give 10 × 10 × 10 × 10 = 10 000.
- If items can't be repeated, the number of choices goes down by one each time: 3 different books can be arranged in 3 × 2 × 1 = 6 ways.
- Deal with restrictions first, for example a code that can't start with 0.
Key terms
- Outcome
- A possible result.
- Systematic
- Organised and in a logical order.
- Product rule
- The total number of combinations is found by multiplying the number of choices for each part.
- Arrangement
- A way of putting items in order.
- Combination
- A selection of items.
Practise Systematic listing and the product rule: 12 questions