unique arrangements

You and 5 friends go to a concert. how many different ways can you sit in the assigned seats? With 6 possible seats, the number of unique arrangements is: 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

In Maricopa County, 5 persons are to be elected to the Board of Supervisors. If 8 persons are candidates, how many different arrangements are possible? We want 8 choose 5, or 8C5. Typing this into the search engine we get 56.