Breathesgelatin--same thing at most SEC schools! When I was at Auburn, most girls seemed to want only 6, maybe 8, of the 14 groups and would drop out of rush or transfer if they didn't get one of those. At Arkansas they wanted 4 of 9 and at Mississippi State, most were aiming for one certain group of the 9 although some girls would settle for 3 of the rest if the first cut them.
Maybe I should say that it's a seller's market for the "upper- and middle-tier" groups but usually, the other groups at the big Southern schools take at least half of quota--which could be 30-35 girls.
Another reason that it's cutthroat is that moms and alums are behind the scenes plotting to get their daughters or favored rushees into their groups. This can be a problem if there are more legacies than the chapter has spaces available (pretty common here) or if the alum club has a list of preferred pledges that clashes with the chapter's list.
Generally, both groups compromise since the chapter needs the alums' help.