Question

2. (6 pts.) Student Engineers Council at a California university has one student representative from each of the five engineering majors (civil, electrical, industrial, materials, and mechanical). In how many ways can Both a council president and a vice president be selected? A president, a vice president, and a secretary be selected? Two members be selected for the President’s Council?

Answer 1

(a) There are 20 ways to select both a council president and a vice president.

(b) There are 60 ways to select both a president, a vice president, and a secretary.

(c) There are 10 ways to select two members for the President’s Council.

Explanation:

All the five engineering majors have one student representative at the Student Engineers Council at a California university.

(a)

Compute the number of ways to select both a council president and a vice president as follows:

As order of selection is important, the number of ways to select both a council president and a vice president is:

`^(5)P_(2)=(5!)/((5-2)!)=20`

Thus, there are 20 ways to select both a council president and a vice president.

(b)

Compute the number of ways to select president, a vice president, and a secretary as follows:

Again as the order of selection is important, the number of ways to select both a president, a vice president, and a secretary is:

`^(5)P_(3)=(5!)/((5-3)!)=60`

Thus, there are 60 ways to select both a president, a vice president, and a secretary.

(c)

Now for two members for the President's Council are to be selected.

As the order of selection is not important, two members can be selected in:

`{5\choose 2}=(5!)/((5-2)!\cdot\ 2!)=(5!)/(3!\ *\ 2!)=10`

Thus, there are 10 ways to select two members for the President’s Council.