3 books of mathematics and 5 books of physics are placed on a shelf so that…

Concept: When items from two or more distinct groups must all stay together as blocks, first arrange the blocks as single units, then separately arrange the items within each block — the total count is the product of the block arrangements and each block's internal arrangements.

1. There are two subject-blocks here: one block of mathematics books and one block of physics books. These two blocks can be placed on the shelf in 2! = 2 ways (mathematics-block first or physics-block first).

2. Within the mathematics block, the 3 mathematics books can be arranged among themselves in 3! = 6 ways.

3. Within the physics block, the 5 physics books can be arranged among themselves in 5! = 120 ways.

4. By the multiplication principle, the total number of arrangements is 2! × 3! × 5! = 2 × 6 × 120 = 1440.

Cross-check: As an independent check, the block order (2!) and the two internal orders (3!, 5!) are three independent, sequential decisions that combine multiplicatively: 2 × 6 = 12, and 12 × 120 = 1440.

So the required number of arrangements is 1440.