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To solve the problem of finding the number of ways to arrange 8 distinct books on a shelf such that 3 specific books are always together, follow these steps:

Step 1: Treat the 3 specific books as a single block

When 3 books must stay together, we merge them into one "entity" (block). This reduces the total number of entities to arrange:
Original books = 8
After merging: 8 - 3 + 1 = 6 entities (the block + 5 remaining individual books).

Step 2: Arrange the 6 entities

These 6 entities are distinct (the block is unique, and the other books are distinct). The number of ways to arrange them is:
[6! = 6×5×4×3×2×1 = 720]

Step 3: Arrange the 3 books inside the block

The 3 specific books within the block are distinct, so they can be ordered among themselves in:
[3! =3×2×1=6] ways.

Step 4: Calculate total arrangements

Multiply the two results to get the total number of valid arrangements:
[6! ×3! =720×6=4320]

Answer: (\boxed{4320})

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