1. **State the problem:** We need to find the number of ways to arrange 3 math books, 5 chemistry books, and 7 physics books on a shelf such that all books of the same subject are kept together. 2. **Group the books by subject:** Treat each subject's books as a single block. So, we have 3 blocks: Math block, Chemistry block, and Physics block. 3. **Arrange the blocks:** The 3 blocks can be arranged in $$3!$$ ways. 4. **Arrange books within each block:** - Math books can be arranged in $$3!$$ ways. - Chemistry books can be arranged in $$5!$$ ways. - Physics books can be arranged in $$7!$$ ways. 5. **Calculate total arrangements:** Multiply the number of ways to arrange the blocks by the number of ways to arrange books within each block: $$3! \times 3! \times 5! \times 7!$$ 6. **Compute factorial values:** - $$3! = 6$$ - $$5! = 120$$ - $$7! = 5040$$ 7. **Final calculation:** $$6 \times 6 \times 120 \times 5040 = 21772800$$ **Answer:** There are $$21772800$$ ways to arrange the books with each subject's books kept together.