You have 15 freshmen, 15 sophomores, 15 juniors, and 15 seniors available.

We assume that the order in which the students are chosen within each "standing" is irrelevant, i.e., we only care about who they are and not the position they were picked.

So, there are _{15}C_{4} ways (combinations) to choose the 4 freshmen, where _{15}C_{4} is the number of possible ways to choose 4 freshmen students out of a total of 15. Recall that _{15}C_{4} = 15!/[4!(15-4)!]=1365.

Similarly, you have _{15}C_{5} different ways to choose the 5 sophomores, _{15}C_{3} to choose the juniors, and _{15}C_{7} different ways to choose the seniors.

Now, multiply these numbers and you have the total number of different ways to perform the task that was assigned.

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...

4.64.6(13 lesson ratings)(13)

0

You pick 4 out 15, 5 out of 15, 3 out of 15, and 7 out of 15. Since all these events are independent, you can use multiplication principle to get the answer.