Examples: You have extra tickets to a show. You are hosting dinner and want exactly as many people as you have chairs. You are driving somewhere and don't want to bother coordinating extra vehicles, so you only want as many people as fit in the car. You are going to play a game for which you need a specific number of people.
The two solutions that present themselves are:
1. Ask one person at a time; get responses immediately. When you have filled up your slots, stop asking people.
2. Send out an informative e-mail or LJ post or something, including the people-limit and a note that the first X people who reply get dibs.
Neither of these seems wholly satisfying to me. With 1, if you wind up needing to wait for responses, getting people lined up can take a long time. It seems to work better for things like theater tickets going unused at the last minute -- if someone isn't contactable right then, you just skip them and go on to the next person, and you've only got one or two slots to fill so it'll probably go pretty quick. But for larger things it seems problematic. The trouble with 2 is that it's rude to tell people about fun things they're not invited to, and somebody is going to wind up being last to find out and therefore left out. Also, I always seem to wind up with not quite the number I was expecting, because someone cancels at the last minute or someone turns up with a friend or whatever. (Neither of these has been a problem in practice, because I don't generally need an exact number for things big enough that I've used method 2, so X - 1 or X + 2 is fine. But they could theoretically be issues.)
I use both of them sometimes, but is there a technique I'm missing that results in rounding up specific numbers of people quickly and efficiently?
(I should perhaps note that, while this is not a theoretical question, it is not a currently relevant question. I am not planning any limited-slot events at this time, so you are not being left out and should not worry about it.)
 That is, without asking a lot of people who aren't interested, wind up being over the people-limit, or otherwise don't come.