Your molecule has three chiral centres:
The maximum number of stereoisomers is
No internal mirror image is possible, so there are no meso compounds to reduce the number of stereoisomers.
There are eight stereoisomers in all.
But the mirror image of your compound is an enantiomer, not a diastereomer.
So there are seven diastereomers.
By looking at the structure of this molecule, you can identify three stereogenic centres.
The general rule for number of stereoisomers is: For
This rule applies to all molecules that do not possess plane of symmetry which is the case of this molecule.
Therefore, for the molecule in question, there will be
Pairs of enantiomers (
Pairs of diastereomers (
So for a given molecule, you will have one pair of enatiomers and 6 pairs of diastereomers (or 7 diastereomers).