Nine friends go to see a movie at the local movie theater and sit in a row together. If there are two friends who refuse to sit next to each other, how many 9-person seating arrangements are possible?  Choose the correct answer:	A) 122,400	B) 162,920	C) 202,180	D) 242,360	E) 282,240
The number of ways to arrange 9 people in a row is 9!   From this we want to subtract all the arrangements where the two friends are next to each other. If we consider them as one unit, then the number of arrangements of this 2-person unit and the 7 other friends is 8! And the number of arrangements of the two friends within this unit are 2 because the two friends can switch places. So the total number of arrangements of the 9 friends with the 2-person unit together is 8!*2   The total number of permutations where these two friends are not seated next to each other is 9! - 8!*2 = 7*8! = 282,240   The answer is 282,240.
<result>E</result>
Nine friends go to see a movie at the local movie theater and sit in a row together. If there are two friends who refuse to sit next to each other, how many 9-person seating arrangements are possible?