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?

Answer 1

2 out of 6 administrators
4 out of 6 others

combinations of 6 taken 2 at a time
= 6!/[ 2!(4!)]
=6*5/2
= 15 combinations of administrators

combinations of 6 taken 4 at a time
= 6!/[ 4!(2!)] = 6*5/2 = 15 combinations of faculty and students
so 15*15 = 225

Answer 2

the other 4 committee members come from the group of 6 faculty and 2 students ... 8C4

number of ways is ... 6P2 * 8C4

Answer 3

8C4 = 8!/[4!(4!)]

= 8*7*6*5/(4*3*2)

= 70
so 15*70 = 1050

Answer 4

Thank You all for your feedback!

I figured out how to solve this problem and the answer was 2100.