iPod touch New ipod displaying all songs from library not just copied ones

Got a new Ipod Touch for my daughter - her music shows our entire library despite that I have only copied over the songs she wants - she can see our entire list but the songs she doesnt want are grayed out and cannot be played. It makes is hard for her to find something though - is this just a setting, display all or not?
Thanks for any help !

yes, Under Music I have turned off Sync and have set it to manually sync music - I thought I would have more control this way.