2014-05-16 09:00:41

Eight friends—Adam, Barry, Carla, Diego, Edith, Frankie, Gio, and Han—are going to a movie together and plan on sitting in a row of eight seats. If Adam and Edith need to be on the ends of the row, how many seating combinations are possible?

The correct answer is 1440.

Explanation: There are 8 seats to fill, and the best way to approach this question is to find the number of people who could theoretically occupy each seat, then multiply them together. Thus, start with 8 spaces:

_ _ _ _ _ _ _ _

Since Adam and Edith need to be on the ends, there are 2 people who could theoretically occupy the first end seat, and 1 person who could occupy the other end (because once Adam or Edith occupies the first seat, the other one has to take the other seat).

2 _ _ _ _ _ _ 1

For the second seat, there are 6 possible occupants, as two of the eight people are already accounted for:

2 6 _ _ _ _ _ 1

Then, there are 5 people that could occupy the third seat (as three are accounted for), 4 that could occupy the fourth seat, and so forth:

2 6 5 4 3 2 1 1

Multiply these together to find the total number of combinations possible: 2 • 6 • 5 • 4 • 3 • 2 • 1 • 1 = 1440.