A club consists of 8 seniors, 7 juniors, and 4 sophomores. A subcommittee consisting of 3 seniors, 2 juniors, and 1 sophomore will be chosen. How many different such subcommittees are there?
Order does not appear to matter here, so you'll be looking for combinations, not permutations.
In how many ways can you choose three of eight seniors?
In how many ways can you choose two of seven juniors?
In how many ways can you choose one of four sophomores?
Where can you go from this...?