Thank you, O Great Khan! Tamerlane got it pretty much exactly right. I would only hope I might do half as well on a question on the Golden Horde!
I saw exactly the same nonsense recently in that great reference work Uncle John’s Bathroom Reader, and I bet that’s where your trivia contest got it from. It’s completely false.
Virtually all hummingbirds, tropical and temperate, lay only two eggs per clutch. Actually most tropical birds only lay two eggs per clutch, while many temperate zone ones lay more. Why exactly this is so is controversial. It is also unknown why temperate hummers lay only two eggs, although it is likely because they are descended from tropical forms.
Hummers, like most birds, will lay two or more clutches per year if time and food resources permit. This is of course more feasible in the tropics where the breeding season is longer.
Hummers are very long-lived for such tiny creatures, and have frequently been documented to live more than 10 years. A female of course will try to breed at least once per year, and more often if possible. So the potential lifetime reproduction could easily be in the range the Tamerlane suggests, although of course the long-term average will be only two surviving offspring per female (as it is in any species where the population is near carrying capacity.)
In almost all hummingbirds, the male takes no part in raising the young. (There are a couple of species in which male care has been documented, but they are definitely an exception.) I would call the mating system “promiscuous” rather than polygynous. Males often perform elaborate flight displays to court females. Some have modified wing feathers that make a special buzz during courtship display. And some tropical forms sing interminably from perches to attract females (though it is very hard to recognize it as “song” since it is so high pitched.) In most species the females probably do come to the males rather than vice versa.
I assume the sex ration at fledging is 50:50, but what the ratio is among adults is very difficult to determine, since males are usually much more conspicuous, and males and females may have somewhat different ecologies (males being territorial at flowers, while females forage more widely). Males are often much more common in collections, but that is probably due to collecting bias.