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Ben has to choose three subjects to study - Leaving Cert Mathematics - Question 3(b) - 2022
Question 3(b)
Ben has to choose three subjects to study. He must pick one subject from each of these three groups: Group A (3 subjects) French Spanish German Group B (4 subjec... show full transcript
Worked Solution & Example Answer:Ben has to choose three subjects to study - Leaving Cert Mathematics - Question 3(b) - 2022
Step 1
How many different choices of three subjects can Ben make, picking one from each group?
Answer
To find the total number of different choices of subjects Ben can make, we will multiply the number of options available in each group together.
Group A has 3 subjects, Group B has 4 subjects, and Group C has 5 subjects. Therefore, the total choices can be calculated as:
Thus, Ben can make 60 different combinations of subjects.
Step 2
Which group should the extra subject be added to, in order to make the number of different choices of three subjects that Ben can make as large as possible? Justify your answer.
Answer
To determine the optimal group to add an extra subject, we will calculate the new total choices for each group:
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Group A: Adding one subject would increase the choices to 4:
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Group B: Adding one subject would increase the choices to 5:
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Group C: Adding one subject would increase the choices to 6:
Comparing these calculations, the biggest increase in choices occurs when the extra subject is added to Group A, resulting in 80 choices. Therefore, the school should add the extra subject to Group A to maximize Ben's options.