What do you call a revue of dancing soldiers? A “troupe” of “troops,” of course. That was kind of a “trope.”
A “troop” is a group of people in the military, and a “troupe” is a group of people in performing arts. They both come from the French troupeau, or “crowd.” A “trope” is a figure of speech, or, in this case, a play on words for artistic effect.
People rarely call three dancers who are part of a company “three troupes.” It’s usually “three members of a troupe.” Yet journalists will often say “three troops” for three members of the military. They’re not supposed to do that, in theory: Both The Associated Press and New York Times stylebooks advise that “troops” has its limits. AP says: “[w]hen the plural appears with a large number, it is understood to mean individuals: There were an estimated 150,000 troops in Iraq. (But not: Three troops were injured.)”
Not everyone agrees with that: Air Force Times regularly uses “troops” for small numbers—“seven Marines were killed and seven troops injured in the accident”—and, truth be told, AP occasionally fails to follow its own advice. Besides, what’s a “large” number?
Garner’s Modern American Usage says that using “troops” for individuals is “standard, despite the inherent ambiguity presented by the collective sense of troop.”
Of course, one soldier does not a “troop” make, under any circumstance. As for “trope,” which is not related to the other two words, we were just going for the laugh.