To form the subcommittee, we first need to choose the chair and vice-chair from the administrators. Since there are 4 administrators and the chair and vice-chair must be administrators, this can be done in (4/2) ways.
After selecting the chair and vice-chair, we need to choose 4 more members from the remaining faculty and students. There are 6 faculty and 4 students remaining, making a total of 10 people to choose from. We need to choose 4 people from these 10, which can be done in (10/4)ways.
Therefore, the total number of ways the subcommittee can be formed is:
\[ \binom{4}{2} \times \binom{10}{4} \]
\[ = \frac{4!}{2! \times (4-2)!} \times \frac{10!}{4! \times (10-4)!} \]
\[ = \frac{4 \times 3}{2 \times 1} \times \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} \]
\[ = 6 \times 210 \]
\[ = 1260 \]
So, the subcommittee can be formed in 1260 ways.
Therefore, the answer is: 1260.
