Blocks of identical copies kept together: A library has two books each with three identical copies, and three other books each with two identical copies. In how many ways can all these books be arranged on a shelf so that copies of the same book are not separated (i.e., kept together)?

Introduction / Context:We have five distinct titles with multiple identical copies per title: two titles have 3 copies each, three titles have 2 copies each. Since identical copies within a title are indistinguishable and must be kept together, each title forms a single block on the shelf.

Given Data / Assumptions:

• Titles: A, B with 3 identical copies each; C, D, E with 2 identical copies each.
• “Not separated” means all copies of a title appear contiguously, acting as one block.
• Identical copies ⇒ internal permutations within a block do not create new arrangements.

Concept / Approach:Treat each title as one block. Then we simply arrange 5 distinct blocks on the shelf.

Step-by-Step Solution:

Verification / Alternative check:Alternative reasoning confirms that any reordering within a block of identical copies is not distinguishable and thus does not increase the count.

Why Other Options Are Wrong:180, 160, 140 imply extra (nonexistent) internal permutations or incorrect block counts.

Common Pitfalls:Treating identical copies as distinct (which would erroneously multiply the count).

Final Answer:120