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-c.

a. There are __ different ways to appoint the officers.

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

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

Answer 1

Answer:

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 four different members. There are 15 qualified candidates, and officers can also serve on the committee. Complete parts a-c.

a) There are __ different ways to appoint the officers.

It is required to obtain the number of ways the officers can be appointed. The order does matter here. Hence, permutations would be used to obtain such value. is obtained as follows:

Part a

The number of ways by which officers can be selected out of 15 people is 32760.

The officers can be selected in a particular order. Hence, the order matters in this example . That is why permutation has been used.

b) How many different ways can the committee be​ appointed.

A committee of four different members cut of a total of 15 eligible members is to be selected . The team can be selected in any particular order since all fifteen candidates have the required to be a part of the team. The order is not important which is the reason the combinations can be used , Hence ,

Part b The number of ways by which a committee can be appointed is 1365.

This time rt was required to obtain the number of ways by which a committee can be app....There are fifteen members and all of them are equally eligible. Hence, the order of selection does not matter.

c) What is the probability of randomly selecting the committee members and getting the four youngest of the qualified​candidates.

It is required. obtain the probability that a committee, after forming, has been selected and has five of the youngest individuals in the committee. It is not quite possible since the committee only consists of four people. Hence, the question of selecting five youngest individuals does not make sense. Thus, the probability is zero.

Part c

The probability of having five youngest candidates in the committee is 0.

The probability is nothing or zero because there are not five members in the committee in the first place. The count of the committee is four. Hence, the probability of having five of the youngest individuals is zero.