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 four different members. There are 15
qualified candidates and officers can also serve on the committee.
Complete parts (a) through (c) below.

a. How many different ways can the officers be appointed?
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

Answer 1

Answer:

a. 32,760 ways

b. 1365 ways

b. 1/1365

Step-by-step explanation:

Given

Number of qualified candidates= 15

Number of Vacancies = 4 ( President, CEO, COO and CFO)

a.

How many different ways can the officers be appointed?

This means that in how many ways can 4 candidates be arranged out of a total of 15.

They keyword here is arranged which means Permutation because the order of arrangement doesn't count.

So,

Number of Appointments = 15P4

Number of Appointment = 1365 ways

b. How many different ways can the committee be appointed?

Here, the order of appointments matters.

So, this means, in his many ways can a committee of 4 be selected out of a total of 15.

The keyword, selection means Combination.

So, number of Appointments = 15C4

Number of Appointments = 1365

c. What is the probability of randomly selecting the committee members and getting the five youngest of the qualified candidates?

There are 1365 ways of choosing the board members and the chance of selecting the 5 youngest members is 1, because there's only one way to select the 5 youngest.

So the probability = 1/1365