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The Product Rule for Counting

The Product Rule for Counting

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Lesson

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8 minute activity

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Tree diagram with two wraps branching to three drinks each, showing six complete lunch outcomes

Counting problems often happen in stages. In the tree diagram, choosing a wrap is one stage and choosing a drink is another.

An option is one possible choice at a single stage, and an outcome is one complete result after all stages are chosen. Each full path on the tree is one lunch outcome.

If every first-stage option can go with every second-stage option, use the product rule. For two stages with aaa options and bbb options, total outcomes are a×ba \times ba×b, so here 2×3=62 \times 3 = 62×3=6.

Questions

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68 exam-style questions

Practice questions

Question 1

2 marks

There are 12 boys and 15 girls in a class. One boy and one girl will be selected to represent the class on the student council. Work out the total number of ways of choosing a boy and a girl.

The Product Rule for Counting Revision Guide

  1. GCSE
  2. /Maths
  3. /The Product Rule for Counting

Revision notes for AQA GCSE Maths The Product Rule for Counting: explanations and worked examples.

Revision guides

Practise questions

1 of 5

A café offers 5 sandwiches and 4 drinks. You choose one sandwich and one drink. How many different meals are possible?