Answer:
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
