Question

Find the number of ways in which five large books, four medium-size books, and three small books can be placed on a shelf so that all books of the same size are together.

• A. \( 5! \times 4! \times 3! \)
• B. \( 6! \times 3! \)
• C. \( 3! \times 4! \)
• D. \( 5! \times 4! \times 2! \)

Hint:

When arranging objects with groups, treat each group as one object and then arrange the objects within the group.

Answer 1

The Correct Option is D

Step 1: Treat same-size books as groups. Treat each group of books as a single item. The number of ways to arrange the groups is \( 3! \) (for the three groups). Within each group, the books can be arranged in \( 5! \), \( 4! \), and \( 2! \) ways for large, medium, and small books respectively.
Step 2: Conclusion. Thus, the total number of ways is \( 5! \times 4! \times 2! \).