If each digit in the set of A = {1,2,3,4,5,6,7,8,9} is exactly used once, in how many ways can the digits be arranged such that the 2 and 5 are not adjacent?	Choices
A) 9! - 8!	B) 8!	C) 9!	D) 7*8!	E) 9! / 2!
The answer should be the (total arrangements) - (arrangements when 2 and 5 are adjacent).   The number of ways to arrange 9 units is 9!   If we think of 2 and 5 as one single unit, the number of arrangements is 8!   Note that 2 and 5 can have two arrangements, so we multiply by 2 to get 2*8!   The total number of valid arrangements is 9! - 2*8! = 9*8! - 2*8! = 7*8!   The answer is 7*8!.
<result>D</result>
If each digit in the set of A = {1,2,3,4,5,6,7,8,9} is exactly used once, in how many ways can the digits be arranged such that the 2 and 5 are not adjacent?