I am trying to work this problem out. I know that the systematic counting principle is used. However, I cannot get the right answer.

Question

For the first part, I took
R=2
N=6
6!/(6-2)! (Permutation).
Answer: 30 choices for the Chair/Vice

The second part, I took
R=2
N=8
Combination form.

From here, I do not know what to do or how to get the correct answer. Please explain how to get the answer. Thank You!

The academic computing committee at a college is in the process of evaluating different computer systems. The committee consists of six ​administrators, six ​faculty, and two students. A six​-person subcommittee is to be formed. The subcommittee must have a chair and vice chair from the​ administrators, the other four committee members have no particularly defined roles from the faculty and students. In how many ways can this subcommittee be​ formed?