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Sophia is selecting a planning committee for her school's annual talent show. The committee must consist of 12 students, with members from both the freshman and sophomore classes. At least two students must be from each class. Which of the following is a viable solution for this situation? (1 point)

6 freshmen and 4 sophomores

O freshmen and 12 sophomores

1 freshman and 11 sophomores

5 freshmen and 7 sophomores

1 answer

To satisfy the requirements for Sophia's planning committee, we need to ensure that there are at least 2 students from each class. Let's evaluate the given options:

  1. 6 freshmen and 4 sophomores: This option has 6 freshmen (which is greater than 2) and 4 sophomores (which is also greater than 2). This option is viable.

  2. 0 freshmen and 12 sophomores: This option has 0 freshmen, which does not meet the requirement of having at least 2 students from the freshman class. This option is not viable.

  3. 1 freshman and 11 sophomores: This option has 1 freshman, which does not meet the requirement of having at least 2 students from the freshman class. This option is not viable.

  4. 5 freshmen and 7 sophomores: This option has 5 freshmen (which is greater than 2) and 7 sophomores (which is also greater than 2). This option is viable.

In summary, the viable solutions from the options provided are:

  • 6 freshmen and 4 sophomores
  • 5 freshmen and 7 sophomores

Thus, both the first and fourth options are viable solutions for the committee.