Numbers change from year to year. I'm not the person to give you an exact number but I remember a number like 80-85% of offered appointments being accepted in years past - in Admissions lingo they call it their "yield."
Around 1600 offered, around 1200 accept each year.
The main part is to be physically, medically, academically, and extracurricular qualified along with the nomination. Class of 2014 - Fully Qualified w/ nomination is 2342. Admitted is 1375. Thats a lot better chances than the near 5000 nominated.
You definitely want to make sure you are fully qualified. If you aren't, admission is impossible