You have to add a property to your backing bean that can read (get) a SelectItem collection (List or array).
There are 2 parts to HTML <OPTION> elements - the value and the label. So it requires a special object to supply both items, even in cases where the label and value are the same. The JSFSelectItem serves that function.
Basically, just iterate your String array and create a SelectItem for each string (there's a single-element constructor that can be used when the label and value are the same string).
For best results, create the SelectItem list when you first need it and cache it in a member variable in the backing bean. That saves overhead.
An IDE is no substitute for an Intelligent Developer.