Numbering books as A,B, C, and D then the variations are:
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120. You do 5*4*3*2*1=120. you multiply the number that you are given for example how many times can books 3 be arranged on a shelf you multiply 3*2*1=6 that is your answer
You can wind up with 10 different pairs of books in your hand, which you can choose from a shelf of 5 books in 20 different ways.
240. 120 ways with the books stacked verticly, and 120 ways with the books stacked horizontaly, or one on top of the other.
8 ! = 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1 = 40320
The number of permutations of 7 things taken 7 at a time is 7 factorial, or 5040.