In how many different ways can you select 4 freshmen, 5 sophomores, 3 juniors, and 7 seniors from a group containing 15 students of each standing?

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.