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:
[tex]_nP_k=\frac{n!}{(n-k)!}[/tex]we have a total of 53 members and the slates contain 4 people, then we have:
[tex]_{53}P_4=\frac{53!}{(53-4)!}=7027800[/tex]Therefore, there are 7,027,800 different slates of candidates.
