A class has 5 freshmen, 4 sophomores, 6 juniors, and 5 seniors. A committee is to be formed by selecting two members from the seniors and one member from each of the other grades. How many different committees are there?
We can pick 2 seniors and there are 5 seniors so 5 x 4 = 20 ways to pick seniors
We can pick 1 freshman and there are 5 freshmen so 5 ways to pick freshman
We can pick 1 sophomore and there are 4 so 4 ways to pick sophomores.
We can pick 1 junior and there are 6 so 6 ways to pick a junior
20 x 5 x 4 x 6 = 2400 different comittees