Student Engineers Council at an Indiana college has one stud

Student Engineers Council at an Indiana college has one student representative from each of the five engineering majors (civil, electrical, industrial, materials, and mechanical).

a) There are ?? ways for both a council president and a vice president to be selected.

b) There are ?? ways for a president, a vice president, and a secretary to be selected.

c) There are ?? ways for two members be selected for the President’s Council with no ordering is implied in the choice.

Solution

A.

Order matters here. Thus, we use permutation.

#ways = 5P2 = 20 [ANSWER]

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B.

Order matters here. Thus, we use permutation.

#ways = 5P3 = 60 [ANSWER]

C.

Order does not matter, so we use combination.

#ways = 5C2 = 10 [ANSWER]