7 people (A, B, C, D, E, F and G) go to a movie and sit next to each other in 7 adjacent seats in the front row of the theater.
How many different arrangements are possible? If A will not sit to the left of F and F will not sit to the left of E. How many different arrangements are possible. Choose one: A) 7!/2 B) 7!/3 C) 7!/4 D) 7!/5 E) 7!/6
7 people can be arranged in a row in 7! ways.   Now, three people among those 7 can be arranged in 3! = 6 ways:   AFE   AEF   EAF   EFA   FAE   FEA   From the 6 arrangements above only EFA is possible (A is not to the left of F and F is not to the left of E), so out of total 7! ways only in 1/6th of the arrangements they are sitting as they want.   Answer: 7!/6 (7!/6).
<result>E</result>
7 people (A, B, C, D, E, F and G) go to a movie and sit next to each other in 7 adjacent seats in the front row of the theater.
How many different arrangements are possible? If A will not sit to the left of F and F will not sit to the left of E. How many different arrangements are possible.