A corporation must appoint a president, chief executive officer (CEO), chief ope

Question

A corporation 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 three different members. There are 15 qualifed candidates, and oficers can also serve on the committee. Complete parts (a) through (c) below a. How many different ways can the officers be appointed? There are dfferent ways to appoint the officers b. How many diferent ways can the committee be appointed? There are different ways to appoint the committee C.What is the probability of randomly selecting the committee members and getting the three youngest of the qualified candidates? P(getting the three youngest of the qualified candidates) Type an integer or a simplified fraction.)

Explanation / Answer

Total number of qualified candidates (n) = 15

A) How many different ways can the officers be appointed?

Solution: Here position of the officers matters so the oreder does count and hence we need to find the permutation

number of officer positions (r) = 4

number of ways = nPr = n!/ (n-r)! = 15! / (15-4)! = 15*14*13*12 = 32760 ways

B) How many different ways the commitee can be appointed?

Solution: A planning commitee has to be appointed with three different members and since there is no specific position to be held ny them, the order doesn't count for this selection and we need to find the combination of r = 3 people from n=15 qualified members(since officers can also serve in the commitee).

number of ways = nCr = 15! / ((15-3)! * (3!)) = 15*14*13 / 3*2*1 = 455

C) Probability of getting three youngest candidate from the qaulified candidate for the commitee?

Solution: Here if you want the youngest candidate for the committee , lets say you will arrange the candidate in ascending order of their age and there will be only one possibility for selecting the first three, so there is only one possible outcome.

Also we can form the committee from 15 people in 455 ways as seen in part B, the total number of possible ways are 455.

probability (of selecting the three youngest candidate ) = 1 / 455

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