Question

A student club consists of 8 freshmen and 7 sophomores. how many different five-person committees can be formed from the students?

Answer 1

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.