Etymology
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Words related to applicable

apply (v.)
late 14c., "join or combine (with); attach (to something), adhere," from Old French aploiier "apply, use, attach" (12c., Modern French appliquer), from Latin applicare "attach to, join, connect;" figuratively, "devote (oneself) to, give attention," from ad "to" (see ad-) + plicare "fold" (from PIE root *plek- "to plait").

The etymological sense is "bring things in contact with one another." In English, from c. 1400 as "use or employ" something for a certain purpose;" from early 15c. of lotions, plasters, etc., "place in contact with the body," also, of one's mental powers or faculties, "put to work at a task or pursuit." Meaning "seek a job by submitting an application for one" is from 1851. A by-form applicate is recorded from 1530s. Related: Applied; applying.
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-able 

common termination and word-forming element of English adjectives (typically based on verbs) and generally adding a notion of "capable of; allowed; worthy of; requiring; to be ______ed," sometimes "full of, causing," from French -able and directly from Latin -abilis. It is properly -ble, from Latin -bilis (the vowel being generally from the stem ending of the verb being suffixed), and it represents PIE *-tro-, a suffix used to form nouns of instrument, cognate with the second syllables of English rudder and saddle (n.).

A living element in English, used in new formations from either Latin or native words (readable, bearable) and also with nouns (objectionable, peaceable). Sometimes with an active signification (suitable, capable), sometimes of neutral signification (durable, conformable). It has become very elastic in meaning, as in a reliable witness, a playable foul ball, perishable goods. A 17c. writer has cadaverable "mortal."

To take a single example in detail, no-one but a competent philologist can tell whether reasonable comes from the verb or the noun reason, nor whether its original sense was that can be reasoned out, or that can reason, or that can be reasoned with, or that has reason, or that listens to reason, or that is consistent with reason; the ordinary man knows only that it can now mean any of these, & justifiably bases on these & similar facts a generous view of the termination's capabilities; credible meaning for him worthy of credence, why should not reliable & dependable mean worthy of reliance & dependence? [Fowler]

In Latin, -abilis and -ibilis depended on the inflectional vowel of the verb. Hence the variant form -ible in Old French, Spanish, English. In English, -able tends to be used with native (and other non-Latin) words, -ible with words of obvious Latin origin (but there are exceptions). The Latin suffix is not etymologically connected with able, but it long has been popularly associated with it, and this probably has contributed to its vigor as a living suffix.

applicability (n.)
"capability of being used," 1650s, from applicable + -ity. Earlier was appliableness (1580s), now obsolete.
inapplicable (adj.)

"incapable of being or not proper to be applied, not suited or suitable," 1650s, from in- (1) "not, opposite of" + applicable. Related: Inapplicably; inapplicability.