Instead of taking the entrance examination of a private university, I'd like to take the entrance examinations of three national universities. The fee of private university is more expensive than that of national universities. I guess this person thinks about the fee and the chances to enter. Usually national universities are more difficult to enter than most of private universities. And there are only chances of three times, because the dates of examination are devided into three days. On the other hand, you can take examinations of private universities as much as you like, because the examination date of each private university is different. So the person may think to get the maximum chances to enter a national university.

Hi. Translation: I want to apply for 1 national university (university funded by Japan) instead of 3 private universities. So 代わりにmeans "instead of" here. "Strange" is 変わっている.