admissibility (n.)

1610s, "allowable," from French admissible, from past-participle stem of Latin admittere "allow to enter, admit, give entrance," from ad "to" (see ad-) + mittere "let go, send" (see mission). The meaning "capable of being allowed entrance" is from 1775; the specific sense of "capable of being used in a legal decision or judicial investigation" is by 1849.

word-forming element making abstract nouns from adjectives and meaning "condition or quality of being ______," from Middle English -ite, from Old French -ete (Modern French -ité) and directly from Latin -itatem (nominative -itas), suffix denoting state or condition, composed of -i- (from the stem or else a connective) + the common abstract suffix -tas (see -ty (2)).

Roughly, the word in -ity usually means the quality of being what the adjective describes, or concretely an instance of the quality, or collectively all the instances; & the word in -ism means the disposition, or collectively all those who feel it. [Fowler]