Question

The academic computing committee at a college is in the process of evaluating different computer systems. The committee consists of seven administrators, six faculty, and four students. A seven person subcommittee is to be formed. The chair and vice chair of the committee must be administrators; the remainder of the committee will consist of faculty and students. In how many ways can this subcommittee be formed?

Answer 1

counting principle
7 choices for chair
6 for vice chain
then \(_{10}C_5\)ways to choose the remaining 5 out of ten