Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

      Lesson details

      Learning outcome

      I can derive the product rule for counting, including when to divide by 2.

      Key learning points

      1. By systematically listing the outcomes for two or more events, a pattern begins to emerge
      2. This pattern can be generalised so that counting possible outcome combinations is quicker
      3. Whether the order of the outcomes matters affects the number of possible outcomes
      4. If order does not matter then repetition can be accounted for when considering the total number of outcomes

      Keywords

      • Trial - A trial is a single, predefined test.

      • Outcome - An outcome is a result of a trial.

      • Systematically - When listing outcomes systematically, they are listed in such a way as to ensure all outcomes are recorded.

      Common misconception

      When using the product rule, pupils may be unsure whether they should divide the product by 2.

      Pay extra attention to the context of the problem. If the order of the two outcomes is irrelevant, then you should divide by two. If each of the two outcomes is allocated to a separate event (e.g. 1st and 2nd) then do not divide by 2.

      Teacher tip

      Some of the examples in the lesson could be enacted to help pupils to visualise what is happening.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

      Loading...

      Prior knowledge starter quiz

      6 Questions

      Q1.
      Two spinners are spun once each. The table shows the outcomes for each spinner. Match each value from the frequency tree to its value.

      An image in a quiz
      Correct Answer:$$a$$,24

      24

      Correct Answer:$$c$$,15

      15

      Correct Answer:$$e$$,3

      3

      Correct Answer:$$g$$,5

      5

      Q2.
      An investigation into some rhubarb plants aims to see if using a special fertiliser (F) increases the chance of the plant yielding rhubarb (R). The diagrams show the results. $$b$$ = .

      An image in a quiz
      Correct Answer: 195

      Q3.
      An investigation into some rhubarb plants aims to see if using a special fertiliser (F) increases the chance of the plant yielding rhubarb (R). The diagrams show the results. $$c$$ = .

      An image in a quiz
      Correct Answer: 240

      Q4.
      An investigation across 60 days explores whether days with rain (R) were more likely to see deer (D) in urban areas. The value of $$y$$ is .

      An image in a quiz
      Correct Answer: 4

      Q5.
      An investigation across 60 days explores whether days with rain (R) were more likely to see deer (D) in urban areas. The value of $$z$$ is .

      An image in a quiz
      Correct Answer: 31

      Q6.
      A game developer tested to see whether a playable character was more likely to win (W) with a rebalance (R) of the character’s stats or not. P(R'W) = .

      An image in a quiz
      Correct Answer: 0.12

      6 Questions

      Q1.
      There are 4 children sat around one table and 8 children sat around another table. The teacher chooses 1 child from each table. In how many different ways could the teacher do this?

      2
      12
      24
      Correct answer: 32
      64

      Q2.
      Here is a restaurant menu for three courses. A customer can choose one starter, one main course and one dessert in different ways.

      An image in a quiz
      Correct Answer: 24

      Q3.
      The restaurant runs out of tiramisu. A customer can choose one starter, one main course and one dessert in different ways now.

      An image in a quiz
      Correct Answer: 12, twelve

      Q4.
      Alex has a pack of 5 cards. He deals one card to himself and deals one card to Sam. In how many different ways can this happen?

      An image in a quiz
      9
      10
      Correct answer: 20
      25
      40

      Q5.
      Izzy has a pack of 7 cards. She takes 2 cards at random from the pack. In how many different ways can this happen?

      An image in a quiz
      13
      14
      Correct answer: 21
      42

      Q6.
      Alex draws 2 different cards from set A and 2 different cards from set B. There are different ways of doing this.

      An image in a quiz
      Correct Answer: 126

      To help you plan your 11 maths lesson on: Combinations, download all teaching resources for free and adapt to suit your pupils' needs...