Applying for VP nom

My DD has been looking into this nomination source as well. Not to sound too pessimistic (I know it does though), what are the actual odds of receiving this nomination?

The Vice President is authorized to nominate individuals to the United States Military, Naval, and Air Force Academies but can not nominate to the U.S. Merchant Marine Academy and does not nominate to the U.S. Coast Guard Academy.

He may have a maximum number of five nominees in attendance at each authorized academy at any one time. Normally, he has one or two vacancies each year.

Let's just say he has 2 vacancies at each of the 3 academies he can nominate for. I don't want to discourage people from trying, but the odds are very long. Personally, I think your time is better spent putting together the best application for your MOC's as possible.
The VP doesn't nominate to USCGA because there is no nomination process for that SA. Not sure why he can't nominate to USMMA but am sure there is a good reason that an MMA grad will probably supply.

As for the the odds being long . . . absolutely. But the nom is also pretty easy and there's only one essay that is probably the same one you've already completed for other MOCs. Your first priorities should be MOC noms. However, I always ask my candidates if they've applied for a VP nom. Failure to do so just because the odds are long (especially when the application is easy) suggests the candidate isn't all that motivated.

And, for the record, a number of years ago one of the folks on this forum actually received a VP nom (and appointment). So, while rare, it does happen. If you don't apply, it definitely WON'T happen for you.:)
Of course the odds are long. When your acceptance rate is in single digits, it's a longshot in general. That means there is attrition at every step of the process.