If each digit in the set of A = {0,1,2,3,4,5,6,7,8,9} is exactly used once, in how many ways can the digits be arranged such that the 2 and 5 are not adjacent?	Answers:	A) 10! / 2!	B) 10! - 9!	C) 9!	D) 10!	E) 8*9!
The answer should be the (total arrangements) - (arrangements when 2 and 5 are adjacent).   The number of ways to arrange 10 units is 10!   If we think of 2 and 5 as one single unit, the number of arrangements is 9!   Note that 2 and 5 can have two arrangements, so we multiply by 2 to get 2*9!   The total number of valid arrangements is 10! - 2*9! = 10*9! - 2*9! = 8*9!   The answer is 8*9!.
<result>E</result>
If each digit in the set of A = {0,1,2,3,4,5,6,7,8,9} is exactly used once, in how many ways can the digits be arranged such that the 2 and 5 are not adjacent?