Counting strategies (Edexcel GCSE Maths): Revision Notes
Counting strategies
What are counting strategies?
Counting strategies are systematic methods used to find all possible combinations or arrangements. When you need to count outcomes, using an organised approach helps ensure you don't miss any possibilities and avoid counting the same thing twice.
Counting strategies are particularly useful in probability, statistics, and combinatorics. They help you work through problems methodically rather than relying on guesswork or random listing.
Systematic listing method
The most effective way to count combinations is to use a systematic approach. This means organising your list in a logical order rather than writing down possibilities randomly.
Step-by-step process
When creating combinations from a set of numbers or items, follow these steps:
- Start with the first item - List all combinations that begin with your first option
- Move to the second item - List all combinations that begin with your second option
- Continue systematically - Keep going through each starting option in order
Example with three-digit numbers
This systematic approach works particularly well when creating number combinations from a limited set of digits.
Worked Example: Creating Three-Digit Numbers
If you have the digits 4, 5, and 6, and need to make different three-digit numbers:
Step 1: Numbers starting with 4: 456, 465
Step 2: Numbers starting with 5: 546, 564
Step 3: Numbers starting with 6: 645, 654
This gives you 6 different three-digit numbers in total.
Worked examples
The following examples demonstrate how systematic listing works in different contexts:
Worked Example: Badge Combinations
James makes badges with:
- 3 colours: Red (R), Green (G), Blue (B)
- 3 shapes: Circle (C), Star (S), Oval (O)
To find all possible badge combinations systematically:
- Red badges: RC, RS, RO
- Green badges: GC, GS, GO
- Blue badges: BC, BS, BO
Total combinations: 9 possible badges
Worked Example: Sports League Matches
In a hockey league with 5 teams (Benfield, Gosforth, Kenton, St Cuthbert's, Sacred Heart), each team plays every other team once.
Systematic listing of matches:
- Team 1 vs: Teams 2, 3, 4, 5 (4 matches)
- Team 2 vs: Teams 3, 4, 5 (3 matches)
- Team 3 vs: Teams 4, 5 (2 matches)
- Team 4 vs: Team 5 (1 match)
Total matches: 10 matches in the league
Key Exam Tips
- Show your systematic strategy - Examiners want to see your organised method, not just the final answer
- Count carefully - Check your list to ensure no combinations are missed or repeated
- Label your work - Make it clear how you've organised your counting
- Answer the question - Always state the total number of combinations at the end
Key Points to Remember:
- Use a systematic method to avoid missing any combinations
- Organise your list in a logical order (alphabetically or numerically)
- Check your work by counting your final list
- Show your strategy clearly in exam questions
- When counting matches or games, remember each pair only plays once