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

Answer 1

To meet the requirement that at least two students must be from each class, we can evaluate the options provided:

A) 5 freshmen and 7 sophomores

• This option has 5 freshmen and 7 sophomores. It satisfies the condition of at least 2 students from each class. (Valid)

B) 1 freshman and 11 sophomores

• This option has only 1 freshman, which does not satisfy the condition of at least 2 students from each class. (Invalid)

C) 6 freshmen and 4 sophomores

• This option has 6 freshmen and 4 sophomores. It satisfies the condition of at least 2 students from each class. (Valid)

D) 0 freshmen and 12 sophomores

• This option has 0 freshmen, which does not satisfy the condition of at least 2 students from each class. (Invalid)

Based on this evaluation, the viable solutions are A) 5 freshmen and 7 sophomores and C) 6 freshmen and 4 sophomores.