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 14 qualified​ candidates, and officers can also serve on the committee. Complete parts​ (a) through​ (c) below.

Answer 1

Using the permutation formula and the combination formula, it is found that:

a) There are 24,024 ways to appoint the officers.

b) There are 1,001 ways to appoint the committee members.

c) $p = \frac{1}{1001}$ probability that the four youngest members are appointed to the committee.

What is the permutation formula?

The number of possible permutations of x elements from a set of n elements is given by:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

What is the combination formula?

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Item a:

For the officers, the order is important, as there are different roles, and 4 officers will be appointed from a set of 14 qualified candidates, hence we use the permutation formula to find the number of ways they can be appointed.

$P_{14,4} = \frac{14!}{10!} = 24024$

Item b:

For the committee, the order is not important, as there are no different roles, and 4 members will be appointed from a set of the 10 remaining candidates, hence we use the combination formula to find the number of ways they can be appointed.

$C_{14,4} = \frac{14!}{4!10!} = 1001$

Item c:

The four youngest is only one possible outcome, hence the probability they are appointed to the committee is given by:

$p = \frac{1}{1001}$

More can be learned about the combination formula at https://brainly.com/question/25821700

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