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For the solution it is allowed to assume that the probability for being born in any month is the same.

This question is trampling on my mind with such a lasting force that I had to get out of bed and ask the kind people of MathStackexchange for some help for I have to attend school in 6 hours and haven't slept a wink $\ddot\smile$

I really can't get beyond the initial stages.

Thank you,

Silenttiffy

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Your question basically asks if you randomly map $n$ items into a set of $12$ items, what is the probability that the mapping is onto (surjective).

This is similar to Number of surjections from $\{1,...,m\}$ into $\{1,...,n\}$

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