Arranging multi-volume books as inseparable blocks: There are 20 books: 4 singles and three multi-volume works of sizes 8, 5, and 3. In how many ways can all books be arranged on a shelf so that volumes of the same work stay together?

Introduction / Context:
When multi-volume works must remain contiguous, treat each work as an inseparable block. The singles remain individual items. Then multiply by the internal permutations of volumes within each block (volumes are distinct).

Given Data / Assumptions:
Singles: 4 books; multi-volume works: sizes 8, 5, 3 (volumes distinct but required to be together).

Concept / Approach:
First, arrange “items” = 4 singles + 3 blocks = 7 items in 7! ways. Next, for each block, order the volumes internally: 8!, 5!, and 3!. Multiply all factors.

Step-by-Step Solution:

Verification / Alternative check:
Counting principle (blocks first, internal orders second) is standard and consistent.

Why Other Options Are Wrong:
7! 8! 4! 3! uses 4! instead of 5!; 7! 6! 5! 3! incorrectly replaces 8! with 6!.

Common Pitfalls:
Forgetting to include internal permutations, or misreading the sizes of the works.

Final Answer:
7! 8! 5! 3!