The word ineligibilities 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: 23
Highest Scoring Words With Friends™ Play In The Letters ineligibilities
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Seven Letter Word Alert: (35 words)
beignet, bellies, belling, belting, besting, billets, billing, bitings, elegist, elegits, gentile, gentles, giblets, glisten, ignites, ileitis, illites, instill, legible, lenites, lentils, lignite, lilting, lintels, listing, selling, sibling, silting, singlet, tellies, telling, tensile, tilings, tilling, tingles