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Tracey is going to choose a main course and a dessert in a cafe - Edexcel - GCSE Maths - Question 15 - 2017 - Paper 2

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Tracey is going to choose a main course and a dessert in a cafe. She can choose from 8 main courses and 7 desserts. Tracey says that to work out the number of diffe... show full transcript

Worked Solution & Example Answer:Tracey is going to choose a main course and a dessert in a cafe - Edexcel - GCSE Maths - Question 15 - 2017 - Paper 2

Step 1

Is Tracey correct? You must give a reason for your answer.

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Answer

No, Tracey is incorrect. To find the total number of ways to choose a main course and a dessert, you must multiply the number of main courses by the number of desserts. In this case, there are 8 main courses and 7 desserts, so the calculation should be:

8×7=568 \times 7 = 56

Thus, Tracey's method of adding the two numbers is not correct.

Step 2

Work out the total number of games played.

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Answer

To determine the total number of games played in which 12 teams each play against each other exactly once, we can use the combination formula to find how many unique pairs of teams can be formed. This is calculated using:

(n2)=n(n−1)2\binom{n}{2} = \frac{n(n-1)}{2}

where ( n ) is the total number of teams. Here, ( n = 12 ), so:

(122)=12×112=66\binom{12}{2} = \frac{12 \times 11}{2} = 66

Therefore, the total number of games played is 66.

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