Corporate Officers and Committees The Newport Medical Supply Company must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a strategic planning committee with four different members. There are 10 qualified candidates, and officers can also serve on the committee.a. How many different ways can the four officers be appointed?b. How many different ways can a committee of four be appointed?c. What is the probability of randomly selecting the committee members and getting the four youngest of the qualified candidates?

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Asked Sep 27, 2019
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Corporate Officers and Committees The Newport Medical Supply Company must appoint a president, chief executive officer (CEO), chief operating officer (COO), and chief financial officer (CFO). It must also appoint a strategic planning committee with four different members. There are 10 qualified candidates, and officers can also serve on the committee.

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

b. How many different ways can a committee of four be appointed?

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

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Expert Answer

Step 1

The total number of officers to be appointed are 4.
President, Chief Executive officer, Chief Financial Officer, Chief operating Officer.

The order of selection is important here as 4 officers have unique designation. So we use Permutation here.

The number of ways of selecting r things out of n thing when order matter is calcualted as shown below. 
The number of ways of selecting four officers from 10 qualified candidates is calculated by substituting r = 4 and n = 10 as shown below

The number of ways of appointing four officers = 5040

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n! "P, (п-г)! 10*9*8*7*6* 5* 4*3*2*1 6 5 4 321 10! 10 Р. (10-4) 10*9*8*7 =5040

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Step 2

The total number of members in committee = 4
Total number of qualified members = 10 (As officers also can be committee members).

Here order of selection is not important so we use combination. The number of ways of selecting r things out of n t...

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n! "C, (n-r)! r! 10*9* 87* 6*5*4*3* 2*1 10! 1C (10 4) 10*9 8*7 4!6*5*4*3* 2*1* 4* 3* 2*1 4*3 21 10*3* 7 210

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