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

5 freshmen and 7 sophomores
5 freshmen and 7 sophomores

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

Answer 1

To determine a viable solution for Sophia's planning committee, we need to consider the requirement that at least two students must be from each class. The total number of students needed is 12, and we need to ensure that the selection satisfies the requirement.

Let's evaluate each of the given options:

1. 5 freshmen and 7 sophomores:

   • Freshmen: 5 (which is at least 2)
   • Sophomores: 7 (which is at least 2)
   • Total: 5 + 7 = 12
   • This option is viable.

2. 6 freshmen and 4 sophomores:

   • Freshmen: 6 (which is at least 2)
   • Sophomores: 4 (which is at least 2)
   • Total: 6 + 4 = 12
   • This option is also viable.

3. 0 freshmen and 12 sophomores:

   • Freshmen: 0 (which does not meet the requirement of at least 2)
   • Sophomores: 12
   • Total: 0 + 12 = 12
   • This option is not viable.

4. 1 freshman and 11 sophomores:

   • Freshmen: 1 (which does not meet the requirement of at least 2)
   • Sophomores: 11
   • Total: 1 + 11 = 12
   • This option is not viable.

Thus, the viable solutions for the planning committee are 5 freshmen and 7 sophomores and 6 freshmen and 4 sophomores.