Source : Webster's Revised Unabridged Dictionary (1913)

Inadmissibility \In`ad*mis`si*bil"i*ty\, n. [Cf. F.
   inadmissibilit['e].]
   The state or quality of being inadmissible, or not to be
   received.

Source : WordNet®

inadmissibility
     n : unacceptability as a consequence of not being admissible
         [ant: {admissibility}]