The word trichotomies is playable in Words With Friends™, no blanks required. Because it is longer than 7 letters, you would have to play off an existing word or do it in several moves.
Words With Friends™ Letter Score: 20
Highest Scoring Words With Friends™ Plays In The Letters trichotomies
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Seven Letter Word Alert: (53 words)
chemist, chooser, chromes, cithers, coheirs, cohorts, cooties, cotters, erotics, hermits, heroics, heroism, hitters, homiest, itchier, meiotic, metrics, metrist, miscite, mistier, mitiest, mitotic, moister, moocher, mooches, moorish, mortise, mothers, mottoes, omitter, osmotic, ostrich, reshoot, rhotics, richest, risotto, scooter, shooter, smother, somitic, soother, sootier, stretch, thermic, thermos, thorite, tithers, titmice, tooters, tootsie, torches, tricots, trisect