The comments on the question are incorrect, as is the answer given in the book. In general, answers printed at the back of a book should never be taken as the absolute truth. There are typos in all books. Even well-known and well-written textbooks have many errata (usually corrected in subsequent printings).

As you said, there are three chiral centres and therefore 8 stereoisomers.

There are no other elements of symmetry present in this molecule which render any of those 8 stereoisomers equivalent.

The comments on the question are incorrect [edit: the offending comments seem to be gone now], as is the answer given in the book. In general, answers printed at the back of a book should never be taken as the absolute truth. There are typos in all books. Even well-known and well-written textbooks have many errata (usually corrected in subsequent printings).

As you said, there are three chiral centres and therefore 8 stereoisomers.

There are no other elements of symmetry present in this molecule which render any of those 8 stereoisomers equivalent.