Question 1206447
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As the other tutors have mentioned, there are 480 arrangements where books A and B aren't next door neighbors.


To form the answer, we'll need the number of ways to get something like ACB, and then we'll place that value over 480.


Consider the pattern ACB to show C is between A and B.
Let X replace this trio.


{A,B,C,D,E,F}
turns into
{X,D,E,F}


There are 4! = 4*3*2*1 = 24 ways to rearrange those 4 letters.
X stands in for ACB but it could also be BCA.
This means we need to double that 24 to 2*24 = 48.


Then we could replace C with either D, E, or F
This means there are 4 choices for the middle book.
48*4 = 192


There are 192 ways to have exactly 1 book placed between books A and B. This is out of the 480 ways total mentioned earlier.


192/480 = (2*96)/(5*96) = 2/5


Answer: 2/5
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