Combinatorics — arranging 5 favorite books between two bookends: if you make a new arrangement every minute (one move per minute), how long to cycle through every possible ordering of the five books?

Introduction / Context:This puzzle checks basic permutations and time calculation. You have 5 distinct books and you want to consider every possible ordering on a shelf. If you change to a new ordering once per minute, the total time equals the number of orderings expressed in minutes.

Given Data / Assumptions:

• Number of distinct books = 5.
• All books are different, so all orderings are unique.
• You make one new arrangement each minute, so 1 arrangement corresponds to 1 minute.
• We assume the goal is to account for all possible permutations of the 5 books.

Concept / Approach:The total number of arrangements of n distinct objects is n!. For n = 5, permutations = 5! = 5 * 4 * 3 * 2 * 1. Convert that count to minutes directly because the rate is 1 arrangement per minute. Finally, convert minutes to hours for comparison with the options.

Step-by-Step Solution:

Verification / Alternative check:Even if you consider the initial layout as one of the arrangements, 120 minutes and 119 minutes are both effectively “about 2 hours.” The closest exact option given is 2 hours.

Why Other Options Are Wrong:

• 1 hour — would imply only 60 permutations (incorrect).
• 3 hours — would imply 180 permutations (too many).
• 4 hours — would imply 240 permutations (double the correct count).

Common Pitfalls:Confusing combinations with permutations; forgetting that order matters on a shelf. Also, mixing up whether to count the starting arrangement does not change the best matching option here.

Final Answer:2 hours