How many ways can 12 different books be arranged in a shelf?

Arthur tells you, the books are already selected.

Also lulu points out, condition "three particular books are never together" is not very clear, I take it to mean only that all three cannot be together, but two together and one apart is fine.

Now going your way, subtract from total ways, the ways in which all three are together.

Total ways are $12!$ and ways in which three are together are $10!\cdot 3!$ so our answer should be $12! - 3! \cdot 10!$