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AQA GCSE · Question 09 · Probability

Callum is making pizza. He can choose three different toppings from:

  • ham (H)
  • sweetcorn (S)
  • onion (O)
  • mushrooms (M).
    List all the possible options for the three toppings. The first one has been done for you: HSO

How to approach this question

1. There are 4 toppings available (H, S, O, M) and Callum must choose 3. 2. This is equivalent to choosing which one of the 4 toppings to leave out. 3. Start with the given combination: HSO. This leaves out M. 4. Now, systematically leave out each of the other toppings one by one. 5. Leave out O: The combination is HSM. 6. Leave out S: The combination is HOM. 7. Leave out H: The combination is SOM. 8. List all the unique combinations found.

Full Answer

HSO (given) HSM HOM SOM
Callum has four toppings to choose from: Ham (H), Sweetcorn (S), Onion (O), and Mushrooms (M). He needs to choose three different toppings for his pizza. This means for each combination, one topping will be left out. We can find all the combinations by considering which topping is excluded each time: 1. Exclude Mushrooms (M): The toppings are Ham, Sweetcorn, Onion. Combination: **HSO** (this was given). 2. Exclude Onion (O): The toppings are Ham, Sweetcorn, Mushrooms. Combination: **HSM**. 3. Exclude Sweetcorn (S): The toppings are Ham, Onion, Mushrooms. Combination: **HOM**. 4. Exclude Ham (H): The toppings are Sweetcorn, Onion, Mushrooms. Combination: **SOM**. The four possible combinations are HSO, HSM, HOM, and SOM.

Common mistakes

✗ Repeating a combination (e.g., writing HSO and SOH as different options - the order does not matter). ✗ Listing combinations with only two toppings or with four toppings. ✗ Missing one or more of the combinations.

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