The word inapplicability 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: 32
Highest Scoring Words With Friends™ Play In The Letters inapplicability
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Seven Letter Word Alert: (32 words)
ability, aclinal, albinal, albinic, albitic, alicant, anaptic, aplitic, bacilli, banally, capably, capital, captain, claypan, illicit, illitic, initial, lacinia, papally, papalty, papilla, pinball, pintail, plainly, platipi, playact, pliably, pliancy, ptyalin, tailpin, tilapia, typical