Question

There are 53 members on the board of directors for a certain non-profit institution. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible? There are _ different slates of candidates possible.please answer the question above.

Answer 1

For this problem the order of selection matter (the first person is the chairperson, the second the first vice chairperson and so on); since this is the case we need to use permutations. The permutation is given by:

`_nP_k=(n!)/((n-k)!)`

we have a total of 53 members and the slates contain 4 people, then we have:

`_(53)P_4=(53!)/((53-4)!)=7027800`

Therefore, there are 7,027,800 different slates of candidates.