sorry to but in,, are you asking ? if we have a free will choice to believe the good news Gospel or not believe it ? ( this website has many more non believers that us true believers )..This is getting tedius.
I can read Koine Greek, and I'm guessing you can't.
In fact, I know you can't, becuase "εκλεγομαι" CANNOT mean "choice/choose", since as you pointed out, "choice" is a noun, and "choose" is a verb. So you again have no clue what you're talking about.
"εκλεγομαι" means "choose" (it's a verb, not a noun).
So for the (what? FOURTH time now), please quote the Bible verse which teaches that man "εκλεγομαι" to believe, or that man "εκλεγομαι" to accept the gospel.