To find how many ways Luna can arrange the books on a shelf with the given constraints, let's break down the problem:

1. Physics Books as a Block: Since the 5 physics books must be arranged together as a block, treat the block of 5 books as a single "item" for now. Inside this block, the 5 physics books can be arranged in any order. The number of ways to arrange the 5 physics books inside their block is: $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$

2. Total Books to Arrange: Now, Luna has 4 different math books and 1 "block" of physics books. In total, there are 5 "items" (4 math books + 1 physics block) to arrange on the shelf. The number of ways to arrange these 5 items is: $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$

3. Total Number of Arrangements: To find the total number of ways to arrange the books on the shelf, multiply the number of ways to arrange the 5 items by the number of ways to arrange the 5 physics books within their block: $5! \times 5! = 120 \times 120 = 14,400$

Thus, Luna can arrange the books on the shelf in 14,400 different ways.

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Would you like more details or have any questions?

Here are 5 related questions:

1. What if Luna wanted the math books to also stay together as a block?
2. How would the arrangement change if Luna could freely arrange both types of books?
3. What if Luna had 6 different physics books instead of 5?
4. How does the concept of permutations apply to this problem?
5. How would the answer change if one of the books was identical to another?

Tip: When working with permutations involving constraints, like keeping items together, think of them as a "block" to simplify calculations.