Question

There are 6 members on a board of directors. If they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?

Answer 1

Answer:

120 different slates of candidates are possible.

Step-by-step explanation:

The order is important.

For example, a slate of John, Rose and Elisa means that John is the chairperson, Rose is the secretary and Elisa is the treasurer. If two of them are exchanged, their roles will also be changed. So we use the permutations formula to solve this question.

Permutations formula:

The number of permutations of x elements from a set of n elements is given by:

$P_{n,x} = \frac{n!}{(n-x)!}$

In this problem, we have that:

6 members will be chosen for 3 roles. So

$P_{6,3} = \frac{6!}{(6-3)!} = 120$

120 different slates of candidates are possible.