A corporation must appoint a president, chief executive officer, chief operating officer and chief financial officer. It also appoint a planning committee with four different members. There are 12 qualified candidates, and officers can also serene on the committee

a) 11,880

b) 495

c) 0.00202

Step-by-step explanation:

Given:

The complete question is as follows:

"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 12

qualified candidates and officers can also serve on the committee.

Find:

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

Solution:

  - The total number of qualified candidates = 12

 - The officers need to be appointed = 4                                                                                                                        (President, Chief Executive Officer, Chief Operating Officer, Chief Financial officer)

  - Here count does count so we use permutations:

  - The number of different ways of appointing Officers = 12P4 = 11,880

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

   The total number of qualified candidates = 12

  The total number of planning committee members = 4  

  Here order does not count as all the planning committee members:

  The number of different ways of appointing Officers = 12C4 = 495

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

  P ( 4 youngest officers ) =  Selecting 4 youngest / Selecting a committee

                                           = 1 / 495

                                           = 0.00202