Each branch has different minimum requirements to apply and differences in the average scores of accepted candidates. So, the chances of winning are not the same among the branches. As far as Army, you can list up to seven college choices (some must be in-state public schools) on your application and there is a winner can be awarded scholarship offers to use at up to three schools on the list. Which schools the winner received scholarships for depends on several factors - I don't think tuition cost is one of them, as far as Army goes. It depends on how many other scholarship winners applied, how many scholarship are allocated, and sometimes, choice of major.