I believe NROTC will allow the applicant to list 1 to 5 schools on the application of which an in-state school has to be in the top 3. That said, I imagine the selection board probably frowns upon picky applicants that specify only one or two schools. Also, the scholarship is contingent on you specifying a school/unit that the placement board is able to place you into based on openings at the time they receive your selection board-approved package. Additionally, the scholarship is contingent on you being accepted into one of the schools into which the NROTC unit has openings. On your application, you specify whether you only want placement into your first choice, or if you’ll accept placement into any of the schools on your application, or any unit to which they can find an opening. I believe that the more flexible you can be, the more likely you are to be selected and placed (certainly the latter, at least). Ideally, you specify 5 schools, are awarded the scholarship, the placement board is able to place you into your first choice unit, and you are accepted by that school. But it’s easy to see how one of the latter two factors may not work out - hence the more schools you list and apply to, the better off your odds are of the stars aligning.
DS has a different problem than others on this thread - he was awarded the Immediate Scholarship Reservation (ISR), but his NROTC Coordinator hasn’t submitted the package yet, so although he’s guaranteed the scholarship and was accepted into all of the schools he listed, the units are filling up fast now and I’m hoping there are still openings in one of the units he listed when the placement board finally receives his package.
Anyway, keep lots of options on the table and best of luck!