DfE statement N5 · Number
Systematic listing and the product rule for counting
Systematic listing and the product rule for counting is content statement N5 of the DfE GCSE mathematics subject content, in the number area. It is on both tiers, with a Higher-only part, and it appears on both the calculator and the non-calculator papers. Below is what the specification actually requires, the 3 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.
What the specification says
The DfE subject content for GCSE mathematics states, verbatim: "Apply systematic listing strategies including use of the product rule for counting." (statement N5). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
Tier
Both tiers, but part of it is Higher only. Foundation covers the statement except for the following, which the DfE prints in bold and reserves for Higher: "including use of the product rule for counting". Everything else in the statement is Foundation content.
Calculator
This turns up on both the non-calculator and the calculator papers, so practise it both ways — the written method for Paper 1 and the efficient calculator route for Papers 2 and 3.
Common mistakes
- Listing outcomes unsystematically, which produces both duplicates and gaps. Fix one element and vary the rest in order.
- Adding the numbers of choices instead of multiplying them: 4 starters and 5 mains give 20 meals, not 9.
- Counting AB and BA as two outcomes when the order does not matter, or as one when it does.
Sample questions (10 of 30)
Nearby statements
Questions people ask
Is systematic listing and the product rule for counting on Foundation or Higher?
Both, but not all of it. The parts the DfE prints in bold — "including use of the product rule for counting" — are Higher only; the rest is Foundation content.
Can I use a calculator for systematic listing and the product rule for counting?
It depends on the paper. Paper 1 is non-calculator; Papers 2 and 3 allow one, and this topic is asked on both kinds.
What is the single most common mistake here?
Listing outcomes unsystematically, which produces both duplicates and gaps. Fix one element and vary the rest in order.
Are these past paper questions?
No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.
Back to Number at Foundation or at Higher.