Examples of students applying to UIUC CS who did not get into the major (one rejected entirely, one admitted to the school but not the CS major):
http://talk.collegeconfidential.com/college-admissions/1858820-rejected-from-my-low-match-saftey-wondering-whether-it-is-time-to-throw-in-the-towel-p1.html
http://talk.collegeconfidential.com/college-admissions/1858898-over-qualified-but-rejected-from-desired-major-at-university-of-illinois.html