At a meeting of 10 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table?  Choose one:
A) 263,320 B) 271,180 C) 282,240 D) 291,470 E) 308,560
10 people can be arranged around a table in 9! ways.   Consider the two chiefs who will not sit together as a single unit.   The number of ways to arrange 9 units around a table is 8!   We need to multiply this by 2 as the two people can be switched in each arrangement.   The total number of ways to arrange the chiefs is 9! - 2*8! = 7*8! = 282,240   The answer is 282,240.
<result>C</result>
At a meeting of 10 Chiefs of Staff, the Chief of Naval Operations does not want to sit next to the Chief of the National Guard Bureau. How many ways can the Chiefs of Staff be seated around a circular table?