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