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Counting problems – practice for Years 7–9

Sample questions on Counting problems with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Maths
Year
Years 7–9
Curriculum area
Problem solving and non-routine tasks

Question types: How many ways?

Rule: Counting problems

When you choose step by step, multiply the numbers of choices at each step.

Without repeats there is one choice fewer at the next step; a number can’t start with 0.

Example: Three-digit numbers from 5 digits without repeats: 5 × 4 × 3 = 60

Watch out: With pairs (handshakes) you count each one twice, so divide by 2: 10 × 9 ÷ 2 = 45.

Sample questions

  1. Question 1 Easy

    The canteen offers 5 soups and 5 main courses. How many different lunches of one soup and one main course can you choose?

    Show the solution
    Answer: 25

    How it works: Every first choice goes with every second choice: 5 × 5 = 25

  2. Question 2 Normal

    How many different two-digit numbers can be written with the digits 1, 5, 6, 8, 9 if no digit may be used twice?

    Show the solution
    Answer: 20

    How it works: The tens digit can be any of 5, the ones digit any of 4: 5 × 4 = 20

  3. Question 3 Hard

    How many different three-digit numbers can be written with the digits 1, 5, 6, 8, 9 if no digit may be used twice?

    Show the solution
    Answer: 60

    How it works: 5 × 4 × 3 = 60

Related topics

All Maths topics

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