Question

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?

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.

Answer 2

In this exercise we have to use the knowledge of probability to know how many people formed the committee, in this way we can say that:

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:

$5 * 4 = 20\\ 20 / 2 = 10$

For the rest, it would be :

$11* 10 * 9 * 8 = 7920\\ 4! = 24\\ 7920 / 24 = 330\\ 330*10=3300$

See more about probability at brainly.com/question/795909