the robotics club has 12 members. there are 3 members from each class: freshmen, sophomores, juniors, and seniors. in each of the freshman and junior classes, 1 member is an engineer and two are in cs; in each of the sophomore and senior classes, 2 are engineers and 1 is in cs. find the number of ways to have a committee of 6 members so that each class and each major is represented on the committee.