Final answer:
In mathematics, arranging four books on a shelf involves permutations due to the order of the books, resulting in 24 possible ways to arrange them.
Explanation:
Permutations are used when the order matters, while combinations are used when the order does not matter. In this case, arranging four books on a shelf involves the order of the books, making it a permutation problem.
To determine the number of ways to arrange the four books, we use the formula for permutations of n items taken r at a time: P(n, r) = n! / (n - r)!. Therefore, the number of ways to arrange four books on a shelf is 4! = 4 x 3 x 2 x 1 = 24.
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