Here is a link to an FAQ on the Princess Cruises website. Just click where it says "Clothing Recommendations" and that will pull up suggested attire for the cruise.
As stated, for casual or informal nights, khakis and a golf shirt, button down, or caribbean themed sportshirt is fine.
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2007 - Majesty of the Seas
2009 - Enchantment of the Seas
2010 - Freedom of the Seas