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 five different members. There are 15 qualified​ candidates, and officers can also serve on the committee. Complete parts​ (a) through​ (c) below. There are nothing different ways to appoint the officers. b. How many different ways can the committee be​ appointed? There are nothing different ways to appoint the committee. c. What is the probability of randomly selecting the committee members and getting the five youngest of the qualified​ candidates? ​P(getting the five youngest of the qualified ​candidates)equals nothing ​(Type an integer or a simplified​ fraction.)

Answer 1

Answer:

(a) There are 32,760 different ways to appoint the officers.

(b) 3003 different ways can the committee be​ appointed.

(c) ​Probability of getting the five youngest of the qualified ​candidates is 0.00033.

Step-by-step explanation:

We are given that 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 five different members.

There are 15 qualified​ candidates, and officers can also serve on the committee.

(a) The number of officers are 4, i.e; A president, chief executive officer​ (CEO), chief operating officer​ (COO), and chief financial officer​ (CFO).

There are 15 qualified candidates.

To find the number of ways to appoint the officers, we will use permutation because here the order of selecting the officer's matters.

So, the number of ways to appoint the officers = $^{15}\text{P}_4$

            =  $\frac{15!}{(15-4)!}$              {$\because ^{n}\text{P}_r = \frac{n!}{(n-r)!}$ }

            =  $\frac{15!}{11!}$  =  32,760 ways

(b) The number of committee numbers to appoint include five members.

There are 15 qualified candidates.

To find the number of ways in which the committee can be​ appointed, we will use combination because here the order of selecting the members doesn't matter.

So, the number of ways to appoint the committee = $^{15}\text{C}_5$

            =  $\frac{15!}{5! \times (15-5)!}$              {$\because ^{n}\text{C}_r = \frac{n!}{r! \times (n-r)!}$ }

            =  $\frac{15!}{5! \times 10!}$  =  3003 ways

(c) The probability of randomly selecting the committee members and getting the five youngest of the qualified​ candidates is given by;

Number of ways of selecting the committee = 3003

Selecting the five youngest of the qualified​ candidates = 1

So, the required probability =  $\frac{1}{3003}$

                                              =  0.00033