Are countries limited to the number of athletes they have in one olympic event?

Question

example; are the united states only allowed to have four athletes representing their country to run in the mens 200 meters?

Answer 1

yes, only a set amount of spots that you can win for your country.  These are usually decided in international tournaments in the years before the games started.

For archery for instance, they have 4 or 5 international tournaments before the Olympics.  There are a total of 64 spot for each male and female.  So the first tournament in the series awarded the first 40 spots, then the next gave out another 10 spot, and so on.  The US got all 3 spots on the men side, but only managed to secure 2 spots on the women side.  Once an athlete secure a spot for their country they can't secure a second spot.