Final answer:
The number of different five-person committees that can be formed from the students is 3003.
Step-by-step explanation:
To find the number of different five-person committees that can be formed from the students, we will use the combination formula.
The combination formula is given by the expression nCr = n! / (r!(n-r)!), where n is the total number of students and r is the number of students we want to choose for the committee.
In this case, we have 8 freshmen and 7 sophomores.
So, the total number of students is 8 + 7 = 15.
We want to form a five-person committee, so r = 5.
Plugging these values into the combination formula:
C = 15!/((5!)(15-5)!)
C = 15! / ((5!)(10!))
C = (15*14*13*12*11*10!) / ((5*4*3*2*1)(10!))
C = (15*14*13*12*11) / (5*4*3*2*1)
C = 3003
Therefore, there are 3003 different five-person committees that can be formed from the students.