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47. Forming a Committee Four members from a 20-person committee are to be selected randomly to serve as chair- person, vice-chairperson, secretary, and treasurer. The first person selected is the chairperson; the second, the vice- chairperson; the third, the secretary; and the fourth, the treasurer. How many different leadership structures are possible

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Answer:

116,280 different leadership structures are possible

Step-by-step explanation:

The order is important.

For example, a Committee of John, Elisa, Laura and Rose means that John is the chairperson, Elisa the vice-chairperson, Laura the secretary and Rose the treasurer. If we exchange John and Elisa, their roles are also exchanged. This means that we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

How many different leadership structures are possible

Permutations of 4 elements from a set of 20. So

[tex]P_{(20,4)} = \frac{20!}{(20-4)!} = 116280[/tex]

116,280 different leadership structures are possible

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