Each event has a cap on the number of athletes a country can send..It seems that all countries have an equal chance to send the same number of athletes depending on how the athletes preform in other competitions, especially in the World Championships.
For example, an Explanation of Figure Skating Allotment and Qualifications and Alpine Skiing Can be found at the related link below.
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There is no quite answer for this question but if i would have to pick a certain nember I would have to say 21, mostly because that is my favorite number!!