Twenty couples attend a Halloween party and enter a competition for the best outfit of the night.

Question:

Twenty couples attend a Halloween party and enter a competition for the best outfit of the night. There are three prizes for the best outfits and prizes are won individually. What is the probability that among the three winners,

(i) there are only women?

(ii) there are two men and a woman?

(iii) there is no couple?

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