Final answer:
To find the total number of arrangements for books on a shelf where books of the same subject should be together, we calculate the permutations of the subject blocks (3!) and multiply this by the permutations within each subject (5! for math and 3! for physics).
Step-by-step explanation:
The question involves arranging different sets of books on a shelf, which is related to permutations and combinations, concepts in mathematics. To solve this, we approach it in steps, first determining the arrangement of books within each subject group and then the arrangement of these groups on the shelf.
Firstly, we consider each set of books as a single block since the books within each subject must stay together. We have 3 blocks: mathematics, chemistry, and physics. These can be arranged in 3! (3 factorial) ways because there are 3 blocks to arrange.
Secondly, we count the ways to arrange books within each block. For the 5 different mathematics books, we have 5! ways. The 2 identical chemistry books can only be arranged in 1 way since they are identical. And for the 3 different physics books, there are 3! ways.
The total number of arrangements is the product of these numbers: 3! × 5! × 1 × 3!. Hence, 3! accounts for the arrangement of the subject blocks, 5! accounts for the arrangement of mathematics books, and 3! is for the physics books.