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vekshin1
2 months ago
8

A corporation must appoint a president, chief executive officer, chief operating officer and chief financial officer. It also ap

point a planning committee with four different members. There are 12 qualified candidates, and officers can also serene on the committee
Mathematics
1 answer:
PIT_PIT [12.4K]2 months ago
6 0

Answer:

a) 11,880

b) 495

c) 0.00202

Step-by-step explanation:

Given:

Here is the full question:

"A corporation needs to select a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It also needs to form a planning committee comprising four distinct members. There are 12

qualified candidates, and the officers can also serve on the committee.

Find:

a. Determine the number of ways to appoint the officers.

Solution:

- Total qualified candidates = 12

 - Number of officers to appoint = 4 (President, Chief Executive Officer, Chief Operating Officer, Chief Financial Officer)

- Since the order matters, we use permutations:

- The number of different arrangements to appoint officers = 12P4 = 11,880

b. Determine the number of ways to select the committee members.

   Total qualified candidates = 12

  The number of planning committee members = 4  

  Here, order doesn't matter, so we use combinations:

  The number of different ways to form a committee = 12C4 = 495

   

c. What is the likelihood of randomly choosing the committee members being the four youngest qualified candidates?

  P ( 4 youngest officers ) =  Chances of selecting 4 youngest / Total number of committees

                                           = 1 / 495

                                           = 0.00202

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