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)

Question

Responses

6 freshmen and 4 sophomores
6 freshmen and 4 sophomores

0 freshmen and 12 sophomores
0 freshmen and 12 sophomores

1 freshman and 11 sophomores
1 freshman and 11 sophomores

5 freshmen and 7 sophomores

Answer 1

To determine which options are viable solutions for Sophia's planning committee, we need to analyze the requirement: the committee must have a total of 12 students, with at least 2 students from each class (freshman and sophomore).

Let's evaluate each option:

1. 6 freshmen and 4 sophomores:

   • Total: 6 + 4 = 10 students.
   • This does not satisfy the requirement of 12 students. Not a viable solution.

2. 0 freshmen and 12 sophomores:

   • Total: 0 + 12 = 12 students.
   • This does not satisfy the requirement of having at least 2 freshmen. Not a viable solution.

3. 1 freshman and 11 sophomores:

   • Total: 1 + 11 = 12 students.
   • This does not satisfy the requirement of having at least 2 freshmen. Not a viable solution.

4. 5 freshmen and 7 sophomores:

   • Total: 5 + 7 = 12 students.
   • This satisfies the requirement of having at least 2 freshmen and at least 2 sophomores. Viable solution.

Based on the analysis, the only viable solution is:

5 freshmen and 7 sophomores.