My son is a Freshman. Loves Purdue and his dorm despite being in the smallest room on campus (Cary Closet). Once accepted, a student can submit a housing contract listing in preference order the type of housing preferred (while there are 9 or so options, due to priority Freshman tend to end up with either a double with a/c or a double without a/c). The deadline for submission is the beginning of May. As long as the contract is submitted by that date, rooms are assigned randomly. There is no advantage to submitting it early. Once that date passes, the contract is binding. That said there was a housing shortage last year, so non-traditional housing was used. Because of this, students were able to be released from their contracts if they elected to move off campus. The contracting process also provides for roommate matching and requesting.
https://www.housing.purdue.edu/housing/contracting/Undergraduate.html