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When i have 1.000.000 different numbers from 1 to 1.000.000 and 400.000 people choose one of them how can i calculate the probability to choose for example 300.000 or 200.000 or x DIFFERENT numbers? In other words how can i calculate the probability of x numbers that not be choosed?

Thanks, Damian

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    So everyone puts his number back into the pot after he drew it? – 2017-02-08
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    I'd use poisson probability that any number independently has zero choices is $\exp(-400000/1000000) = \exp(-.4) = .6703$ so 67.3% of numbers will be unchosen - poisson is justified for this case – 2017-02-08

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I'd use poisson probability that any number independently has zero choices is $exp(−400000/1000000)=exp(−.4)=.6703$

so 67.3% of numbers will be unchosen - poisson is justified for this case - the result was born out by a simulation I ran

if you want to know the probability of a prescise count, such as 670,300, then you would take that binomial probability, .6703, and use the normal sistribution of the binomial distribution to estimate

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To follow up Cato, that means the number of empty cells will almost always be within $\sqrt{1000000}=1000$ of 670300.