Four members from a 12 -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?

11880 ways

Step-by-step explanation:

We can solve this problem in two ways. I'm going to show you how to do both.

We have 12 persons and are to choose a chairperson, a vice chairperson, secretary and a treasurer. So we are picking 4 members our of 12 persons.

From this 12, when we pick out one member, we are left with 11members. From 11, if we pick out another one, we have 10 left. From 10, if we pick out another member we have 9 left.

Such that

12 x11 x10x 9= 11880

These are the total different leadership structures possible.

Another way to solve this is by permutation method.

nPr

12!/(12-4)!

= 12!/8!

= 11880 ways