Princess's "Cruise Answerbook" indicates that a typical ten-day cruise has two formal nights and three semiformal nights, but we had the reverse (three formal nights and two semiformal nights) on my only ten-day cruise. It seems to depend, to some degree on how many passengers are members of the Captain's Circle. We had a lot of Captain's Circle members on that cruise, so they had to hold separate Captain's Circle cocktail parties for each dining room (on separate nights) in order to accommodate all of the members. This might have triggered the third formal night.
I just returned from a twelve-night cruise aboard MV Royal Princess that had several semiformal nights in addition to three formal nights. Several posters here have indicated that MV Grand Princess no longer has a semiformal night on her seven-night Caribbean itineraries, but I have not heard that any other ships have dispensed with semiformal nights. Thus, I would plan on two or three semiformal nights on a 10-day Princess cruise.