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?

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Mathematics

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17 December, 23:10

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?

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Dixon · Answer 1

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.