India centrally allocates seats to federal public engineering colleges, including the IITs, via a clearinghouse which makes it safe for candidates to truthfully report their preference rankings over 600+ programs. Since applicants may not carefully rank programs that are not allocation relevant, we introduce a methodology to model applicant preferences using only plausibly allocation-relevant comparisons in their rankings. Using 2015 administrative records, we estimate a mixed nested choice model over programs with random distance-aversion coefficients. Women are more distance-averse than men, and this gender gap is larger among affirmative action (AA) candidates; women's mean distance penalty is 66% larger among non-AA candidates and 104% among AA candidates. Gender and AA status also shift preferences across academic streams. Replacing women’s fitted distance sensitivity with men’s closes roughly one-third of the model-implied attainable-program-value gender gap overall and about two-fifths of the gap among AA candidates.