Question

100 pigeons P1, ..., P100 fly into 500 labelled holes h1, ..., h500. Each pigeon picks...

100 pigeons P1, ..., P100 fly into 500 labelled holes h1, ..., h500. Each pigeon picks a hole uniformly at random and independently from the choices of the other pigeons.

What is the probability that at least one hole contains at least 3 pigeons. The answer is supposed to be 0.4361298523736379.

Any other answer is wrong, in correct please make sure your answer matches the answer provided.

Math   Statistics-And-Probability   
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Random pigeonholing 100 pigeons p1,…,p100 fly into 500 labelled holes h1,…,h500. Each pigeon picks a hole...
Random pigeonholing 100 pigeons p1,…,p100 fly into 500 labelled holes h1,…,h500. Each pigeon picks a hole uniformly at random and independently from the choices of the other pigeons. What is the probability that at least one hole contains at least 2 pigeons. What is the probability that at least one hole contains at least 3 pigeons.
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