List every possible combination or arrangement in an organised order so none are missed or repeated. It is a Foundation topic, aimed at grade 2. Free questions with answers are on this page. Worked examples show each line before you try the questions.
Listing outcomes is not a memory test — it is a grid in disguise. For two coins, fix the first as H and vary the second (HH, HT), then fix the first as T (TH, TT). Four outcomes, all equally likely if the coins are fair. Missing TH because it 'feels the same' as HT is the classic error: they are different outcomes.
When two choices are independent, multiply: 4 shirts and 3 pairs of trousers give 4×3=12 outfits. When you are making numbers from digits without replacement, there are fewer choices for the second slot: three digits for a 2-digit number, used once each, is 3×2=6.
A two-way table or a sample-space grid keeps the list honest. If the question asks for a probability afterwards, the denominator is the number of outcomes you just listed.
Objectives
Fix the first choice, then list every second choice under it.
If every option in the first list pairs with every option in the second, multiply.
Red then blue is a different pair from blue then red only when order matters.
Key points
List all the ways of choosing one item from each of two groups.
List all the arrangements (orders) of a small set of digits or letters.
Use the product rule: number of choices for the first thing × number of choices for the second.
Pick out from your list the ones that satisfy a condition (even, odd, over 500…).
Worked examples
Example 1
A lunch deal offers 3 breads and 2 fillings. Every bread can take every filling. How many different lunches are there?
2 marks
Each of the 3 breads can take 2 fillings.
3 × 2 = 6.
The result is 6.
Answer: 6
Common slips
Slip: Each of the 3 breads can take 1 filling. Every bread pairs with every filling, not with just one.
Slip: 3 + 2 = 5. The choices are multiplied. Adding them misses most of the lunches.
Slip: The result is 5. That is the number of choices added together, not the number of lunches.
Example 2
A meal has 2 starters, 2 mains and 3 desserts. How many different three-course meals can be made?
2 marks
2 × 2 = 4 starter and main pairs.
4 × 3 = 12.
The result is 12.
Answer: 12
Common slips
Slip: 2 + 2 = 4 starter and main pairs. Each starter goes with each main, so multiply.
Slip: 4 + 3 = 7. Each pair goes with each dessert, so multiply again.
Slip: The result is 7. That does not match the working above it.
Example 3
A code has two digits. Each digit is 3, 5 or 7, and a digit can be used twice. How many different codes are there?
3 marks
There are 3 choices for the first digit.
There are also 3 choices for the second digit, because a digit can repeat.
3 × 3 = 9.
Answer: 9
Common slips
Slip: There are 3 choices for both digits together. Each digit is chosen separately, so each one has its own choices.
Slip: There are 2 choices for the second digit. A digit can be used twice, so none of the choices are used up.
Slip: 3 × 2 = 6. That is the answer when digits cannot repeat, which this question allows.
Questions and answers
GCSE Maths systematic listing questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
A lunch deal offers 3 breads and 4 fillings. Every bread can take every filling. How many different lunches are there?
Show answer
Answer: 12
Each of the 3 breads can take 4 fillings.
3 × 4 = 12.
M1 — Each of the 3 breads can take 4 fillings.
A1 — Answer 12
Question 2 Easy2 marks
A club has 4 members. Two of them are chosen to be captains and the order does not matter. How many different pairs can be chosen?
Show answer
Answer: 6
Each of the 4 members pairs with 3 others: 4 × 3 = 12.
Each pair has been counted twice, once in each order.
M1 — Each of the 4 members pairs with 3 others: 4 × 3 = 12.
A1 — Answer 6
Question 3 Medium2 marks
A meal has 2 starters, 3 mains and 3 desserts. How many different three-course meals can be made?
Show answer
Answer: 18
2 × 3 = 6 starter and main pairs.
6 × 3 = 18.
M1 — 2 × 3 = 6 starter and main pairs.
A1 — Answer 18
Question 4 Medium2 marks
A club has 5 members. Two of them are chosen to be captains and the order does not matter. How many different pairs can be chosen?
Show answer
Answer: 10
Each of the 5 members pairs with 4 others: 5 × 4 = 20.
Each pair has been counted twice, once in each order.
M1 — Each of the 5 members pairs with 4 others: 5 × 4 = 20.
A1 — Answer 10
Question 5 Hard2 marks
A meal has 3 starters, 3 mains and 4 desserts. How many different three-course meals can be made?
Show answer
Answer: 36
3 × 3 = 9 starter and main pairs.
9 × 4 = 36.
M1 — 3 × 3 = 9 starter and main pairs.
A1 — Answer 36
Question 6 Hard2 marks
A club has 6 members. Two of them are chosen to be captains and the order does not matter. How many different pairs can be chosen?
Show answer
Answer: 15
Each of the 6 members pairs with 5 others: 6 × 5 = 30.
Each pair has been counted twice, once in each order.
M1 — Each of the 6 members pairs with 5 others: 6 × 5 = 30.
A1 — Answer 15
Question 7 Exam-style3 marks
A meal has 3 starters, 4 mains and 2 desserts. How many different three-course meals can be made?
Show answer
Answer: 24
3 × 4 = 12 starter and main pairs.
12 × 2 = 24.
The result is 24.
M1 — 3 × 4 = 12 starter and main pairs.
M1 — 12 × 2 = 24.
A1 — Answer 24
Common mistakes
Most lost marks on this topic are one slip.
Adding the number of choices.
Independent choices are multiplied.
Listing only one second choice for each first choice.
Every first choice pairs with every second choice.
Counting a reversed pair twice when order does not matter.
Decide whether order matters before you list.
Spot the slip
How many outcomes are there for 2 breads and 3 fillings?
6
5
3
Show the slip
6 Each bread pairs with each filling, so multiply.
Exam tips
Be ready to do this without a calculator. Paper 1 is the non-calculator paper.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write your list in columns or rows so the pattern is visible; an examiner can then see it is systematic.
Finish with the count and a quick product-rule check — it catches a missing item.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.