I got an offer for an exchange program and I have paid the deposit, which isn’t cheap. The application deadline (which I was only informed a few hours ago) is due in two weeks, on 2nd March. I have to get a letter of reference from a professor by then, but it’s hard to contact them right now because public holidays (lasting for around 6 days) are starting on the day after tomorrow. If I do it after the holiday then I’ll have less than 5 days until the deadline. I have emailed a prof, asking for an appointment but haven’t got back any response. Is it ok to ask a few more profs in case I don’t get any replies or get rejected by said prof?