It depends on the school. At some schools, the number of non-direct-admit prospective engineering and computer science majors who reach the application stage (completion of specified prerequisites) is significantly greater than the number of spaces available to them. Of course, it can also depend on the specific major – some may be more popular relative to capacity than others. At other schools, the entrance to major thresholds are much lower, or the majors are open (i.e. accept all who pass the prerequisites).
http://talk.collegeconfidential.com/discussion/comment/19854939/#Comment_19854939 shows admission thresholds for computer science at various schools, although you should verify on school web sites in case of changes.