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Students at a school must choose one subject from Option 1 and one from Option 2 - OCR - GCSE Maths - Question 16 - 2017 - Paper 1

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Students at a school must choose one subject from Option 1 and one from Option 2. The school offers two languages, French and Spanish. The subjects are given in thi... show full transcript

Worked Solution & Example Answer:Students at a school must choose one subject from Option 1 and one from Option 2 - OCR - GCSE Maths - Question 16 - 2017 - Paper 1

Step 1

Total number of subject combinations

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Answer

To find the total number of subject combinations, we multiply the number of subjects from both options:

  • Option 1: 4 subjects (French, Art, Music, Economics)
  • Option 2: 4 subjects (Spanish, Geography, History)

Thus, the total combinations are:

4imes4=164 imes 4 = 16

Step 2

Subject combinations with exactly one language

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Answer

To find the combinations with exactly one language, we consider:

  1. French with non-language subjects: 3 combinations (French + Art, French + Geography, French + History)
  2. Spanish with non-language subjects: 3 combinations (Spanish + Art, Spanish + Geography, Spanish + History)

So the number of combinations with exactly one language is:

3+3=63 + 3 = 6

Step 3

Calculate the percentage

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Answer

To calculate the percentage of combinations with exactly one language, use the formula:

extPercentage=(Number of combinations with one languageTotal combinations)×100 ext{Percentage} = \left( \frac{\text{Number of combinations with one language}}{\text{Total combinations}} \right) \times 100

Substituting the values gives:

Percentage=(616)×100=37.5%\text{Percentage} = \left( \frac{6}{16} \right) \times 100 = 37.5\%.

Thus, the percentage of all subject combinations that have exactly one language is 37.5%.

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