To form a viable solution for Sophia's planning committee for the annual talent show, the committee must consist of 12 students, with at least 2 students from the freshman class and at least 2 students from the sophomore class. This means we have to ensure that the total number of students from both classes adds up to 12, while also meeting the minimum requirement for each class.
A simple way to approach this problem is to distribute the remaining students after fulfilling the minimum requirement. For example:
- Freshmen: 2 students
- Sophomores: 2 students
- Remaining students (12 total - 4 already selected) = 8 students
The remaining 8 students can be chosen freely from either class, as long as the total number of freshmen and sophomores adds up to 12. Here are two examples of viable solutions:
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Example 1:
- Freshmen: 2
- Sophomores: 10
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Example 2:
- Freshmen: 6
- Sophomores: 6
Here's a more detailed breakdown of the solution paths you can take, ensuring that at least 2 students come from each class:
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Choose 2 freshmen and 2 sophomores
- Freshmen = 2
- Sophomores = 2
- Total = 4
- Choose 8 more students from either freshmen or sophomores to reach a total of 12.
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Choose a range of students that meets the requirement:
- Freshmen = 3, Sophomores = 9 (Total = 12)
- Freshmen = 4, Sophomores = 8 (Total = 12)
- Freshmen = 5, Sophomores = 7 (Total = 12)
- Freshmen = 6, Sophomores = 6 (Total = 12)
- Freshmen = 7, Sophomores = 5 (Total = 12)
- Freshmen = 8, Sophomores = 4 (Total = 12)
- Freshmen = 9, Sophomores = 3 (Total = 12)
- Freshmen = 10, Sophomores = 2 (Total = 12)
Any configuration that adheres to the conditions set (at least 2 from each class) and totals 12 students is a viable solution.
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