Question

Six friends go to a movie theater. In how many different ways can they sit together in a row of six empty seats?

A. 7,200
B. 720
C. 72
D. 46,656

Answer 1

Explanation:

There are 6 people and 6 seats. This means that any one of the 6 can take any one of the 6 seats. When person 1 sits in seat 1, there are 5 people left for the remaining 5 seats. When person 1 sits in seat 2, there are 4 people left for the remaining 4 seats. The catch here is that when there are, say, 5 seats left, those 5 people can "mix it up" so many different ways; but there will always be 1 less person when one sits down. This is a factorial problem:

6*5*4*3*2*1 = 720, choice B