Incredibly difficult for most, and in the cases of some of the most prestigous with famous highly sought instructors unless you have a track record of winning and placing well in respected competitions and could easily gain not only admission but likely win key scholarships at less competitive schools, it is unlikely one would gain admission on first try depending on who else is trying for spots that year. In some cases there are almost already informal unofficial nods and expextations at who will get a place and the auditions for placement in some artist'a studios sometimes almost seems more like a formality, in addition to open screening in case some incredible talent pops out of nowhere for the audition.So certain national conservatories ie in France, UK, Russia, some pacific rim countires and top tier schools in US like Julliard, Curtis, certain Universities w famous artists in residence, you sort of see a better of the best to best of the best going to those places, and many times, unbelievable talent has a difficult time gaining admission depending on who else auditioned that year.