I think it is possible to end up with no invites to preference. One way would be to be released by every sorority. Based on what my daughter knew of other's invites two years ago when she went through, I'd say this does not happen often. It seemed like the PNM's in her group at least had one of the two chapters back that are lower performing in formal recruitment. But I'm sure there are some PNMs that get released by every sorority.
But another way it could happen is if after the open house round the PNM ranks these sororities last, ends up with a full plate of 16 sororities back which excludes say the 3 or 4 weakest recruiting sororities. However, over the course of philanthropy and sisterhood, this PNM gets released by all the other sororities she had at 16. No invites left for Preference.
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