Question

Student Engineers Council at an Indiana college has one student representative from each of the five engineering majors (civil, electrical, industrial, materials, and mechanical). In how many ways can a. Both a council president and a vice president be selected? b. A president, a vice president, and a secretary be selected? c. 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 a president, a vice president, and a secretary. c. There are 10 ways to select two members for the President's Council.

Step-by-step explanation:

a. To select both a council president and a vice president, we can use the multiplication principle. There are 5 choices for the council president since there is one representative from each engineering major. After the president is selected, there are 4 choices remaining for the vice president. Therefore, the total number of ways to select both a council president and a vice president is 5 * 4 = 20.

b. To select a president, a vice president, and a secretary, we can again use the multiplication principle. There are 5 choices for the president, 4 choices for the vice president, and 3 choices for the secretary. Therefore, the total number of ways to select a president, a vice president, and a secretary is 5 * 4 * 3 = 60.

c. To select two members for the President's Council, we can use combinations. Since order doesn't matter, we can use the formula for combinations: C(n, r) = n! / (r! * (n - r)!), where n is the total number of members (5) and r is the number of members to be selected (2). Plugging in the values, we get C(5, 2) = 5! / (2! * (5 - 2)!) = 10.