Chance of x Red balls sharing a bucket with a Green ball

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The discussion centers on calculating the probability of x green balls sharing a bucket with a red ball when 34 red balls are randomly placed in 237 buckets containing n green balls. The key formula involves permutations and combinations to determine the likelihood of this event. Participants emphasize the necessity of understanding these mathematical concepts to derive the probability accurately. A clear approach to solving this problem is essential for effective homework assistance.

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Superposed_Cat
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If I have 237 buckets, and there are n green balls distributed randomly over those buckets, and I put 34 new red balls randomly in those 237 buckets, what is the formula for the probability that x green balls share a bucket with a red ball?

Any help appreciated.
 
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