# 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

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Answer: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.Step-by-step 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=12Number of Posts=4As the order is important the number of ways are identified using Permutations given as [tex]Number\,\ of\, ways=^{12}P_4\\Number\,\ of\, ways=\frac{12!}{(12-4)!}\\Number\,\ of\, ways=\frac{12!}{8!}\\Number\,\ of\, ways=11880[/tex]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=12Number of Posts=4As the order is not important the number of ways are identified using Combinations given as [tex]Number\,\ of\, ways=^{12}C_4\\Number\,\ of\, ways=\frac{12!}{(12-4)!4!}\\Number\,\ of\, ways=\frac{12!}{8!4!}\\Number\,\ of\, ways=495[/tex]So the number of ways in which the candidates can be appointed as members of the planning committee are 495.