GCSE-ready- Home
- Lessons
- GCSE & IGCSE Mathematics
- The product rule for counting
The product rule for counting
How many different meals can you make from a menu? Multiply instead of listing them all.
Listing systematically
To list every combination, fix the first choice and run through all the others, then move on. This stops you missing or repeating any.
The product rule
If there are m ways to do one thing and n ways to do another, there are m × n ways to do both.
3 starters and 4 mains: 3 × 4 = 12 meals.
3 starters and 4 mains: 3 × 4 = 12 meals.
Repeats or not
A 4-digit PIN using 0 to 9 with repeats allowed: 10 × 10 × 10 × 10 = 10 000.
If digits cannot repeat: 10 × 9 × 8 × 7 = 5040.
If digits cannot repeat: 10 × 9 × 8 × 7 = 5040.
A café offers 3 drinks, 5 sandwiches and 2 snacks. How many different meal deals with one of each are there?
- Use the product rule.
- 3 × 5 × 2
- = 30
Answer: 30
Multiply the number of choices at each stage. Check whether repeats are allowed; if not, each stage has one fewer option.
Check you have got it
Answer 6 quick questions with instant marking. If you get one wrong, GCSE-ready shows you why and gives you another go. It is free, and you do not need an account.