"choose from" vs "choose out of" vs "choose among"

I tried to form a sentence like this:

X chooses Y from three Zs.

X chooses Y out of three Zs.

I couldn't choose which one is better, and after googling found question on en.se and thread on forum.wordreference.com and ended up with three options:

• choose from
• choose out of
• choose among

In the question on en.se dcaswell's answer states:

With choose from you can select many items. With choose among you are selecting a single item.

What about choose out of? What is the difference between three options?

The preposition from contains two meanings that might apply:

3. Indicating the source or provenance of someone or something:

or

7. Indicating separation or removal:

The preposition among contains a meaning that applies:

4. Indicating a division, choice, or differentiation involving three or more participants:

The preposition out of contains a meaning that combines from and among:

3. From among (a number):

All three expressions could correctly be interpreted with the same meaning:

• X chooses Y from three Zs can mean X chooses Y from among three Zs.
• X chooses Y out of three Zs can mean X chooses Y from among three Zs.
• X chooses Y among three Zs can maean X chooses Y from among three Zs.

Still, each of the prepositions can also imply separate nuances according to their respective definitions.

The etymologies suggest different root ideas:

from suggests movement to another location:

Old English fram "from, since, by, as a result," originally "forward movement, advancement," evolving into sense of "movement away," from Proto-Germanic *fra "forward, away from" (cognates: Old Saxon, Old High German, Gothic fram "from, away," Old Norse fra "from," fram "forward"), from PIE *pro-mo-, suffixed form of *pro (see pro-).

out of suggests movement out and away

Old English of, unstressed form of æf (prep., adv.) "away, away from," from Proto-Germanic *af (cognates: Old Norse af, Old Frisian af, of "of," Dutch af "off, down," German ab "off, from, down"), from PIE *apo- "off, away" (see apo-). Primary sense in Old English still was "away," but shifted in Middle English with use of the word to translate Latin de, ex, and especially Old French de, which had come to be the substitute for the genitive case. "Of shares with another word of the same length, as, the evil glory of being accessory to more crimes against grammar than any other." [Fowler]

among suggests connection to a group:

early 12c., from Old English onmang, from phrase on gemang "in a crowd," from gemengan "to mingle" (see mingle). Collective prefix ge- dropped 12c. leaving onmong, amang, among. Compare Old Saxon angimang "among, amid;" Old Frisian mong "among."

The verb choose complements all three of those root meanings:

• What I choose moves toward me from the original group.

• What I choose also moves out and away from its original group.

• What I choose was part of the original group of choices.

Dcaswell's interpretation is legitimate: The preposition among tends to stand alone in its implication of exclusivity with reference to the original group, but that implication is not absolute in any way.