The academic computing committee at a college is in the process of evaluating different computer systems. the committee consists of five administrators, seven faculty, and four students. a six 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?

There are 3,300 different ways to select the committee.

First, we need to determine the total number of ways the 6 members can be selected.

For the chair and vice chair, it would be 5 x 4 = 20, but then that has to be divided by 2. (Because the order doesn't matter)
20 / 2 = 10

For the rest, it would be 11 x 10 x 9 x 8 = 7920, but again divide it by 4! because the order doesn't matter.
7920 / 24 = 330

To find the total ways for both, multiply 10 by 330 to get 3300.

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