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