The Collaborative International Dictionary of English v.0.48:
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. [1913 Webster]WordNet (r) 3.0 (2006):
inadmissibility n 1: unacceptability as a consequence of not being admissible [ant: admissibility]