Final answer:
The number of different five-person committees with two freshmen and three sophomores is calculated by finding the combination of two freshmen from the total number of freshmen and multiplying it by the combination of three sophomores from the total number of sophomores.
Step-by-step explanation:
The question asks about the number of different five-person committees that can be formed from two groups of students: freshmen and sophomores. Given that the committee must consist of two freshmen and three sophomores, this is a problem that involves combinations. To solve, we calculate the number of ways to choose two freshmen out of the total number of freshmen and multiply this by the number of ways to choose three sophomores out of the total number of sophomores.
Assuming there are n freshmen and m sophomores, the number of different committees can be found using the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number, k is the number chosen, and ! denotes factorial.
The calculation would be C(n, 2) * C(m, 3), which gives us the total number of ways to form such committees. Make sure to replace n and m with the actual numbers of freshmen and sophomores available to get the final answer.