Question

There are 12 members on the board of directors for the Newport General Hospital. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible?

Answer 1

11880 different slates of candidates are possible.

Explanation:

The order is important in this problem.

That is, John, Elisa, Laura and Rose means that John is the chairperson, Elisa the first vice chairperson, Laura the second vice chairperson and Rose the secretary. If we exchange John and Elisa, for example, it means that their roles also have changed.

So we use the permutations formula to solve this problem.

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

`P_((n,x)) = (n!)/((n-x)!)`

How many different slates of candidates are possible?

Four roles in a set of 12 members. So

`P_((12,4)) = (12!)/((12-4)!) = 11880`

11880 different slates of candidates are possible.