Question

Four members from a ​"55"person committee are to be selected randomly to serve as​ chairperson, 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?

Answer 1

8,185,320 different leadership structures

Explanation:

Since the order at which the members of the committee are chosen matters, this is a permutation of 4 out 55 people and it is given by:

`n=(55!)/((55-4)!)=55*54*53*52 \\\\n=8,185,320`

8,185,320 different leadership structures are​ possible.