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The answer is B. 24.
To find the number of ways to arrange 4 books on a shelf, we use the formula for permutations which is:
n! / (n - r)!
Where n is the total number of books (4 in this case) and r is the number of books being arranged (also 4 in this case).
Using the formula:
4! / (4-4)! = 4! / 0! = 4 x 3 x 2 x 1 = 24
Therefore, there are 24 different ways to arrange 4 books on a shelf.