Product rule for counting Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Product rule for counting questions. See exactly how to solve problems on product rule, sample space, three stages, counting numbers.

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GCSE Higher70 questionsStep-by-step solutions
Question 1
1 markeasy
There are 33 tops and 55 pairs of shorts. How many different outfits can be made?

Worked solution

  1. Each top pairs with each pair of shorts

    3 tops, 5 shorts3\ \text{tops},\ 5\ \text{shorts}

    For each of the 3 tops there are 5 possible shorts.

  2. Product rule: multiply

    3×53\times5

    The product rule says multiply the number of choices at each stage.

  3. Work it out

    3×5=153\times5=15

    So there are 15 outfits.

Answer
1515
Question 2
1 markeasy
A cafe has 44 sandwiches and 33 drinks. How many sandwich-and-drink combinations are there?

Worked solution

  1. Sandwich choices then drink choices

    4 sandwiches, 3 drinks4\ \text{sandwiches},\ 3\ \text{drinks}

    For each sandwich there are 3 drinks.

  2. Multiply

    4×34\times3

    Use the product rule.

  3. Work it out

    4×3=124\times3=12

    So there are 12 combinations.

Answer
1212
Question 3
1 markeasy
A phone case comes in 22 colours and 66 sizes. How many different cases are there?

Worked solution

  1. Colour choices then size choices

    2 colours, 6 sizes2\ \text{colours},\ 6\ \text{sizes}

    For each colour there are 6 sizes.

  2. Multiply

    2×62\times6

    Use the product rule.

  3. Work it out

    2×6=122\times6=12

    So there are 12 cases.

Answer
1212
Question 4
1 markeasy
A coin is tossed and a dice is rolled. Use the product rule to find how many outcomes there are.

Worked solution

  1. Coin outcomes then dice outcomes

    2 coin, 6 dice2\ \text{coin},\ 6\ \text{dice}

    The coin has 2 outcomes and the dice has 6.

  2. Multiply

    2×62\times6

    Use the product rule.

  3. Work it out

    2×6=122\times6=12

    So there are 12 outcomes.

Answer
1212
Question 5
1 markeasy
A menu has 55 starters and 44 mains. How many two-course meals are possible?

Worked solution

  1. Starter choices then main choices

    5 starters, 4 mains5\ \text{starters},\ 4\ \text{mains}

    For each starter there are 4 mains.

  2. Multiply

    5×45\times4

    Use the product rule.

  3. Work it out

    5×4=205\times4=20

    So there are 20 meals.

Answer
2020

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