Question

There are 12 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

12C3 = 12!/(9!)(3!) = 10 x 11 x 12 / 6 = 220.

Answer 2

Answer: There are 220 different possible slates of candidates.

Explanation:

Since we have given that

Total number of members on a board of directors = 12

Number of posts to be elected = 3

As follows:

Chairperson, a secretary, and a treasurer.

So, Number of different slates of candidates that are possible is given by

`^(12)C_3\\\\=(12!)/(3!(12-3)!)\\\\=(12!)/(3!){9!}\\\\=220`

Hence, there are 220 different possible slates of candidates.