Question 1201073: A corporation must appoint a president, chief executive officer (CEO), chief financial officer (CFO) and chief operating officer (COO). It must also appoint a planning committee with six different members. There are 12 qualified candidates, and officers can also serve on the committee.
(i) How many different ways can the officers be appointed?
(ii) What is the probability of randomly selecting the officers and getting the youngest candidate a president?
(iii) How many different ways can the committee be appointed?
(iv) What is the probability of randomly selecting the committee members and getting the six youngest of the qualified candidates?
Answer by asinus(45)   (Show Source):
You can put this solution on YOUR website! Certainly, let's break down the calculations for each part:
**i) How many different ways can the officers be appointed?**
* We have 12 candidates for 4 positions: President, CEO, CFO, and COO.
* The order of selection matters.
* This is a permutation problem.
* Number of ways to appoint officers = 12P4 = 12! / (12-4)! = 12! / 8! = 12 * 11 * 10 * 9 = 11,880 ways
**ii) What is the probability of randomly selecting the officers and getting the youngest candidate a president?**
* There is only 1 youngest candidate.
* For the President position, there is 1 favorable outcome (youngest candidate) out of 12 possible candidates.
* For the other 3 positions (CEO, CFO, COO), there are no restrictions.
* Probability = (1/12) * (11/11) * (10/10) * (9/9) = 1/12
**iii) How many different ways can the committee be appointed?**
* We need to select 6 members out of 12 candidates.
* The order of selection does not matter.
* This is a combination problem.
* Number of ways to appoint the committee = 12C6 = 12! / (6! * (12-6)!) = 12! / (6! * 6!) = 924 ways
**iv) What is the probability of randomly selecting the committee members and getting the six youngest of the qualified candidates?**
* There is only 1 favorable outcome (selecting the 6 youngest candidates) out of 924 possible combinations.
* Probability = 1/924
Let me know if you have any other questions or would like to explore different scenarios!
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