It depends.
Do you have your degree already?
If so, you would apply directly to OCS.
If not, you would apply to the STA-21 program, or BDCP/NUPOC (
http://www.navy.com/joining/educatio...rgraduate.html) to complete your degree prior to attending OCS.
You could also become a LDO or CWO.
Maybe it's different in the nuke community, but from what I've seen your recruiter is being very generous with that percentage.
Direct Commission applicants (those with degrees) have been recently picked up at a rate of anywhere between 1-30 percent depending on the community.
I don't know the percentage for the other programs, but it's not uncommon for people to have to apply more than once before being selected.
Best thing you can do is get the best Evals you can, and get recommendations from your chain of command.