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Systematic listing practice questions with answers

Foundation · Grade 2 · Non-calculator

A second set of systematic listing questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

A lunch deal offers 2 breads and 5 fillings. Every bread can take every filling. How many different lunches are there?

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Answer: 10

  1. Each of the 2 breads can take 5 fillings.
  2. 2 × 5 = 10.
  • Method (1): Each of the 2 breads can take 5 fillings.
  • Accuracy (1): Answer 10

Question 2 Easy

A code has two different digits chosen from the digits 3, 5 and 7. How many different codes are there?

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Answer: 6

  1. There are 3 choices for the first digit.
  2. One digit is used up, so 2 choices are left for the second.
  • Method (1): There are 3 choices for the first digit.
  • Accuracy (1): Answer 6

Question 3 Medium

A lunch deal offers 4 breads and 5 fillings. Every bread can take every filling. How many different lunches are there?

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Answer: 20

  1. Each of the 4 breads can take 5 fillings.
  2. 4 × 5 = 20.
  • Method (1): Each of the 4 breads can take 5 fillings.
  • Accuracy (1): Answer 20

Question 4 Medium

A code has two digits. Each digit is 3, 5, 7 or 8, and a digit can be used twice. How many different codes are there?

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Answer: 16

  1. There are 4 choices for the first digit.
  2. There are also 4 choices for the second digit, because a digit can repeat.
  • Method (1): There are 4 choices for the first digit.
  • Accuracy (1): Answer 16

Question 5 Hard

A code has two different digits chosen from the digits 3, 5, 7 and 8. How many different codes are there?

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Answer: 12

  1. There are 4 choices for the first digit.
  2. One digit is used up, so 3 choices are left for the second.
  • Method (1): There are 4 choices for the first digit.
  • Accuracy (1): Answer 12

Question 6 Hard

A lunch deal offers 5 breads and 6 fillings. Every bread can take every filling. How many different lunches are there?

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Answer: 30

  1. Each of the 5 breads can take 6 fillings.
  2. 5 × 6 = 30.
  • Method (1): Each of the 5 breads can take 6 fillings.
  • Accuracy (1): Answer 30

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 13 marks

A club has 7 members. Two of them are chosen to be captains and the order does not matter. How many different pairs can be chosen?

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Answer: 21

  1. Each of the 7 members pairs with 6 others: 7 × 6 = 42.
  2. Each pair has been counted twice, once in each order.
  3. 42 ÷ 2 = 21.
  • Method (1): 7 × 6 = 42.
  • Method (1): Halve it, because each pair is counted twice.
  • Accuracy (1): Answer 21

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

A lunch deal offers 3 breads and 3 fillings. Every bread can take every filling. How many different lunches are there?

  1. 9
  2. 6
  3. 3
Show answer

9 The result is 9.

Check 2

A meal has 2 starters, 2 mains and 2 desserts. How many different three-course meals can be made?

  1. 8
  2. 4
  3. 6
Show answer

8 The result is 8.

Check 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?

  1. 9
  2. 6
  3. 3
Show answer

9 The result is 9.

Check 4

A club has 7 members. Two of them are chosen to be captains and the order does not matter. How many different pairs can be chosen?

  1. 21
  2. 42
  3. 49
Show answer

21 The result is 21.

Check 5

A lunch deal offers 4 breads and 4 fillings. Every bread can take every filling. How many different lunches are there?

  1. 16
  2. 8
  3. 4
Show answer

16 The result is 16.

Check 6

A meal has 4 starters, 2 mains and 3 desserts. How many different three-course meals can be made?

  1. 24
  2. 8
  3. 9
Show answer

24 The result is 24.

Check 7

A code has two different digits chosen from the digits 3, 5 and 7. How many different codes are there?

  1. 6
  2. 9
  3. 3
Show answer

6 The result is 6.

Check 8

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?

  1. 10
  2. 20
  3. 25
Show answer

10 The result is 10.

Check 9

A lunch deal offers 6 breads and 3 fillings. Every bread can take every filling. How many different lunches are there?

  1. 18
  2. 9
  3. 3
Show answer

18 The result is 18.

Check 10

A meal has 3 starters, 3 mains and 2 desserts. How many different three-course meals can be made?

  1. 18
  2. 9
  3. 8
Show answer

18 The result is 18.

Check 11

A code has two digits. Each digit is 3, 5, 7 or 8, and a digit can be used twice. How many different codes are there?

  1. 16
  2. 12
  3. 4
Show answer

16 The result is 16.

Check 12

A club has 8 members. Two of them are chosen to be captains and the order does not matter. How many different pairs can be chosen?

  1. 28
  2. 56
  3. 64
Show answer

28 The result is 28.

Check 13

A lunch deal offers 5 breads and 5 fillings. Every bread can take every filling. How many different lunches are there?

  1. 25
  2. 10
  3. 5
Show answer

25 The result is 25.

Check 14

A meal has 2 starters, 5 mains and 2 desserts. How many different three-course meals can be made?

  1. 20
  2. 10
  3. 9
Show answer

20 The result is 20.

Check 15

A code has two different digits chosen from the digits 3, 5, 7 and 8. How many different codes are there?

  1. 12
  2. 16
  3. 4
Show answer

12 The result is 12.

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