AQA · GCSE · Mathematics

    Course version: 8300 · Version from Sept 2015

    Enumerate sets and combinations of sets systematically, using tables,…

    Full specification wording

    Probability: enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams

    To enumerate means to list all possible outcomes or members of sets systematically so none are missed or repeated.

    Checked against the AQA 8300 specification (opens in a new tab) on .

    • Point 6 of 10
    • 3 key terms

    Study notes

    From the checked teaching notes for this specification point.

    The idea

    To enumerate means to list all possible outcomes or members of sets systematically so none are missed or repeated. A table or grid is ideal when two choices combine, such as listing pairs from rolling two dice. A Venn diagram is useful for showing sets, their intersections and unions, and counting elements in each region. Systematic working means following a fixed order, like fixing the first outcome and varying the second. For sets A and B, Venn diagram regions represent A only, B only, both, and neither.

    What earns the marks

    • Defines enumeration as listing all possible outcomes or members of sets in a systematic order.
    • Constructs a table or grid to list combinations of two or more sets without missing or repeating any outcome.
    • Interprets a Venn diagram to show sets, including their intersection and union, and to count elements in each region.
    • Applies a fixed order when listing, such as fixing the first item and varying the second, to ensure completeness.
    • Checks that the total number of listed outcomes matches the product of the numbers of choices where appropriate.

    Common mistakes and how to put them right

    • Listing outcomes in a random order and missing some combinations.

      Put it right: Use a table, grid or fixed order so every combination appears exactly once.

    • Counting an outcome twice when it belongs to both sets.

      Put it right: Place it in the intersection region of the Venn diagram and count it once.

    • Confusing the union of two sets with the intersection.

      Put it right: The union contains everything in either set, while the intersection contains only elements in both sets.

    Exam tips

    • Before answering, sketch a quick table, grid or Venn diagram to organise the information.
    • Check that the number of listed outcomes matches what you expect from the number of choices.
    • In Venn diagram questions, label each region and check that the counts add up to the total.

    Try the lesson

    The start of the Probability: enumerate sets and combinations of sets systematically, using tables, grids, Venn diagrams lesson, made from checked teaching notes for this specification point.

    Have a go first

    A café offers a sandwich choice of cheese or ham and a drink choice of tea or juice. Using a systematic list, how many different sandwich-and-drink combinations are possible?

    Listen

    To enumerate means to list all possible outcomes or members of sets systematically so none are missed or repeated. A table or grid is ideal when two choices combine, such as listing pairs from rolling two dice. A Venn diagram is useful for showing sets, their intersections and unions, and counting elements in each region. Systematic working means following a fixed order, like fixing the first outcome and varying the second. For sets A and B, Venn diagram regions represent A only, B only, both, and neither. A strong answer earns marks for these points. Defines enumeration as listing all possible outcomes or members of sets in a systematic order. Constructs a table or grid to list combinations of two or more sets without missing or repeating any outcome. Interprets a Venn diagram to show sets, including their intersection and union, and to count elements in each region. Applies a fixed order when listing, such as fixing the first item and varying the second, to ensure completeness. A common slip: Listing outcomes in a random order and missing some combinations. Instead, use a table, grid or fixed order so every combination appears exactly once. Exam tip: Before answering, sketch a quick table, grid or Venn diagram to organise the information.

    See it

    A top-down flowchart. The top node reads 'Choose a systematic method' and branches into two paths. The left path goes to 'Table or grid for two choices', then to 'Fix the first outcome and vary the second', then to 'Every combination listed exactly once', then to 'Check total matches product of numbers of choices'. The right path goes to 'Venn diagram for sets', then to 'Regions: A only, B only, both, neither', then to 'Count each element once; intersection counted once', then to 'Check counts add up to the universal set'.
    It shows the two systematic methods — a table or grid and a Venn diagram — and the checks that each lists or counts every outcome exactly once.

    Key words

    Say what each word means before you turn the card.

    Systematic listing of outcomes

    Try answering aloud or in your head before turning the card.

    Tables and grids for combinations

    Try answering aloud or in your head before turning the card.

    Venn diagrams for sets and their regions

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    See every definition
    Systematic listing of outcomes
    Listing all possible outcomes or members of sets systematically so none are missed or repeated, following a fixed order.
    Tables and grids for combinations
    A table or grid is ideal when two choices combine, such as listing pairs from rolling two dice.
    Venn diagrams for sets and their regions
    A diagram useful for showing sets, their intersections and unions, and counting elements in each region.

    Label the diagram

    Some boxes have lost their names. Pick the right name for each number.

    The diagram again, with 3 boxes numbered instead of named. A top-down flowchart. The top node reads 'Choose a systematic method' and branches into two paths. The left path goes to 'Table or grid for two choices', then to 'Fix the first outcome and vary the second', then to 'Every combination listed exactly once', then to 'Check total matches product of numbers of choices'. The right path goes to 'Venn diagram for sets', then to 'Regions: A only, B only, both, neither', then to 'Count each element once; intersection counted once', then to 'Check counts add up to the universal set'.

    • 1Box 1

    • 2Box 2

    • 3Box 3

    0 of 3 labelled

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