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The product rule for counting finds the total number of outcomes by multiplying the number of choices at each stage. This topic applies it to combinations of events. It's a core topic in GCSE and iGCSE Maths with Edexcel and the other major boards. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
Multiply the number of choices at each stage. If there are 4 ways to do the first thing and 3 for the second, there are 12 altogether. If items cannot repeat, reduce the count by one each time.
Before you start
This builds directly on systematic listing and index laws. You meet it at Higher tier. Keep it sharp for probability of combined events. It is part of the Number strand.
What you learn
The product rule for counting turns ‘how many ways’ questions into a multiplication. It scales to huge numbers you could never list by hand. When items are used once each, the number of choices shrinks by one at each stage. When there’s a restriction, handle the restricted position first, then fill the rest. The course works through the product rule, arrangements without repetition and counting with restrictions. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Product Rule for Counting is part of the Number strand of our free GCSE maths courses, studied in Higher tier. There are 3 teaching sections and 2 fully worked examples, plus 3 sets of check questions. It sits alongside Reverse Percentages, Rounding & Estimation, Significant Figures & Truncation, Standard Form and Standard Units & Measures in the same strand. The Number revision engine gives you as many extra questions as you want, tracked on your skill tree.
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