4. We want to create a committee of students and faculty to determine how to improve online and hybrid courses. The college president has determined the following roles will be filled by faculty: chair, vice chair, and secretary. There will be 5 student representatives selected to sit on the committee as well, with no specific roles. a. If there are 12 faculty and 43 students to choose from, how many ways can we select this committee made up of chair, vice chair, secretary, and 5 student reps? b. If 5 of the college faculty have 10+ years experience, how many ways can we select this committee made up of chair, vice chair, secretary, and 5 student reps, assuming that the chair, vice chair, and secretary are all faculty with 10+ years experience? c. If we randomly select a committee, what is the probability they have 3 faculty with 10+ years of experience as the chair, vice chair, and secretary and 5 student reps?

4. We want to create a committee of students and faculty to determine how to improve online and hybrid courses. The college president has determined the following roles will be filled by faculty: chair, vice chair, and secretary. There will be 5 student representatives selected to sit on the committee as well, with no specific roles. a. If there are 12 faculty and 43 students to choose from, how many ways can we select this committee made up of chair, vice chair, secretary, and 5 student reps? b. If 5 of the college faculty have 10+ years experience, how many ways can we select this committee made up of chair, vice chair, secretary, and 5 student reps, assuming that the chair, vice chair, and secretary are all faculty with 10+ years experience? c. If we randomly select a committee, what is the probability they have 3 faculty with 10+ years of experience as the chair, vice chair, and secretary and 5 student reps?

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Description: 4. We want to create a committee of students and faculty to determine howto improve online and hybrid courses. The college president hasdetermined the following roles will be filled by faculty: chair, vice chair, andsecretary. There will be 5 studen

MATLAB: An Introduction with Applications

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Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

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4. We want to create a committee of students and faculty to determine how
to improve online and hybrid courses. The college president has
determined the following roles will be filled by faculty: chair, vice chair, and
secretary. There will be 5 student representatives selected to sit on the
committee as well, with no specific roles.
a. If there are 12 faculty and 43 students to choose from, how many
ways can we select this committee made up of chair, vice chair,
secretary, and 5 student reps?
b. If 5 of the college faculty have 10+ years experience, how many ways
can we select this committee made up of chair, vice chair, secretary,
and 5 student reps, assuming that the chair, vice chair, and secretary
are all faculty with 10+ years experience?
c. If we randomly select a committee, what is the probability they have
3 faculty with 10+ years of experience as the chair, vice chair, and
secretary and 5 student reps?

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