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30 / 33

20 people choosing numbers between 1 and 100

First number can be anything

2nd number must be different from first: probability 99/100 = 0.99

3rd number must be different from 1st and 2nd: probability 98/100 = 0.98

…..

Probability that all 20 are different =

     0.99 x 0.98 x ….  0.81 = 0.13

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