Final answer:
To find the number of ways 5 books can be arranged taken 3 at a time, we use permutations. The formula is P(5, 3) = 5! / (5 - 3)! which equals 60 different arrangements.
Step-by-step explanation:
The question at hand is about calculating the number of ways 5 books can be arranged when taken 3 at a time. This type of problem is a permutation problem because the order in which the books are arranged matters.
To determine the answer, we can use the permutation formula which is given by P(n, r) = n! / (n - r)!. In this formula 'n' represents the total number of items (in this case, 5 books) and 'r' represents the number of items to choose (in this case, 3 books).
Therefore, using the formula:
P(5, 3) = 5! / (5 - 3)! = (5 × 4 × 3 × 2 × 1) / (2 × 1) = 5 × 4 × 3 = 60
Thus, there are 60 different ways to arrange 5 books taken 3 at a time.