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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.

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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.

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A task has aaa options at stage one and bbb options at stage two. How is the total number of outcomes calculated?

The Product Rule for Counting Revision Guide

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

Revision notes for Edexcel GCSE Maths The Product Rule for Counting. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Maths (1MA1) specification, so the content matches what's examinable rather than general Maths background.

Revision guides

Recurring Decimals to FractionsFractional and Negative IndicesThe Product Rule for CountingRepeated Percentage ChangeExpanding Triple BracketsParallel and Perpendicular LinesInequalities on GraphsSimilar Shapes (Area and Volume)Enlarging with Negative Scale FactorsCircle TheoremsCumulative FrequencyBox PlotsCapture Recapture

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?