If an applicant applies to two colleges whose admissions are completely correlated (i.e. their criteria and processes are identical), then the probability of acceptance by either one is not increased at all. In reality, however, the two admissions are not fully correlated (i.e. the admission by one doesn’t guarantee admission by the other) and the joint probability of acceptance by either one is higher. The less correlated the two admissions are, the higher the joint probability. To maximize this joint probability, an applicants should choose a small set of less correlated colleges. As others have said, if the set is too large, the probability of acceptance to each individual college would likely suffer due to limitation on resources, which in turn negatively affects the joint probability of acceptance by any one college.