This almost happened to me back in the 80s. I returned to all but one of my top choices between 18 and 12, so I had eliminated 5 of the weaker sororities. By the time I got to Preference, I only had 1 invite, but luckily one I was very happy with and received a bid. But I could have easily received no invites. This was much more common back in the 80s. With RFM, it is supposed to push you down more quickly to chapters that are realistic for the PNM. But I'm sure sometimes the numbers just don't work out right.
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