AlphaGamUGAAlum, the University of Kansas Greek Life / Panhellenic site says that they "guarantee":
http://www.kugreek.org/panhellenic_qa.html#18
Will I automatically get into a chapter by the end of the week?
KU has a very low occurrence of women who are not matched to a chapter for one reason or another. The average percentage of women who didn’t match over the last three years is about 4%. While we can’t guarantee that you’ll match to a chapter for the whole week, if you participate in the Preference round (the last round of recruitment) and you maximize your options when you rank the chapters you visited that night, and we will guarantee that you will become a member of one of those chapters.
Note that the PNM has to make it to Preference and has to maximize her options when she ranks after Pref.