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?

Question

A. 1 freshman and 11 sophomores
B. 5 freshmen and 7 sophomores
C. 6 freshmen and 4 sophomores
D. 0 freshmen and 12 sophomores

Answer 1

To satisfy the requirement that the planning committee must consist of 12 students, with at least 2 students from each class, we can evaluate each option:

A. 1 freshman and 11 sophomores

• This does not meet the requirement of having at least 2 students from the freshman class. Not viable.

B. 5 freshmen and 7 sophomores

• This meets the requirement of having at least 2 freshmen and 2 sophomores. Viable.

C. 6 freshmen and 4 sophomores

• This also meets the requirement of having at least 2 freshmen and 2 sophomores. Viable.

D. 0 freshmen and 12 sophomores

• This does not meet the requirement of having at least 2 freshmen. Not viable.

From the options given, the viable solutions are B (5 freshmen and 7 sophomores) and C (6 freshmen and 4 sophomores).