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Why does this happen?

Imagine 35 people in a line

First birthday can be anything

2nd birthday must be different from first: probability 364/365 = 0.997

3rd birthday must be different from 1st and 2nd: probability 363/365 = 0.995

…..

Probability that all 35 are different =

     0.997 x 0.995 x ….  0.907 = 0.19

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