A medical supply company must appoint a president, chief executive officer (CEO)

Question

A medical supply company must appoint a president, chief executive officer (CEO), chief operating officer(COO), and chief financial officer (CFO). It must also appoint a planning, committee with five different members. There are 12 qualified candidates, and officers can also serve on the committee. Complete parts (a) through (c) below. a. How many different ways can be officers be appointed? There are _______ different ways to appoint the officers. (Simplify your answer.) b. How many different ways can the committee be appointed? There are ________ different ways to appoint the committee. (Simplify your answer.) c. What is the probability of randomly selecting the committee members and getting the five youngest of the candidates? P(getting the five youngest of the qualified candidates) = __________ (Type an integer or a simplified fraction.)

Explanation / Answer

a.

There are 4 positions which can be offered and all of these positions are different and there is a pool of 12 guys to choose from.

The number of ways to appoint officers would be given by,

N = C(12,4)*4! = 11,880

b.

There are 5 members of committee and a pool of 12 persons to choose from and all of these positions are equivalent. The number of ways would be given by,

N = C(12,5) = 792

c.

There is only 1 combination such that the 5 youngest of qualified candidates get become the members of committee. Hence the required probability would be given by,

P = 1/792

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