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DfE statement N5 · Number

Systematic listing and the product rule for counting

part HigherEither paper

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.

— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement N5

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)

N5 · Systematic listing and the product rule for countingQuestion 1 of 10 · 0 correct
Practice mode· no pressure · hints available

Number

N5

Advanced

A café meal deal is one sandwich, one snack and one drink. There are 4 different sandwiches, 3 different snacks and 2 different drinks to choose from. Work out how many different meal deals are possible.

💡 Hints:
Foundation worksheetHigher worksheetFoundation number practiceHigher number practice

Nearby statements

N3Inverse operations and priority of operationsN4Factors, multiples, primes, HCF and LCMN6Powers and rootspart HigherN7Calculating with roots and indicespart Higher

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.

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