Question

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

Answer 1

Part a: The number of ways in which the candidates can be appointed on the executive posts are 11880.

Part b: The number of ways in which the candidates can be appointed as members of the planning committee are 495.

Explanation:

As the complete question is not given a similar question is found online and is attached herewith.

Part a: Number of ways in which 12 candidates can be appointed for President, Chief Executive Officer, Chief Operating Officer and Chief Finance Officer.

Number of Candidates=12

Number of Posts=4

As the order is important the number of ways are identified using Permutations given as

`Number\,\ of\, ways=^(12)P_4\\Number\,\ of\, ways=(12!)/((12-4)!)\\Number\,\ of\, ways=(12!)/(8!)\\Number\,\ of\, ways=11880`

So the number of ways in which the candidates can be appointed on the executive posts are 11880.

Part b: Number of ways in which 12 candidates can be appointed as members of the planning committee.

Number of Candidates=12

Number of Posts=4

As the order is not important the number of ways are identified using Combinations given as

`Number\,\ of\, ways=^(12)C_4\\Number\,\ of\, ways=(12!)/((12-4)!4!)\\Number\,\ of\, ways=(12!)/(8!4!)\\Number\,\ of\, ways=495`

So the number of ways in which the candidates can be appointed as members of the planning committee are 495.