# Probability that seems easy but not!

Hi, here is the question

if there are 25 people, what is the likelihood that at least one of them is born in each month of the year?

not any formula I can think of, sorry

I have tried everymethod, consider number of month that not contain birthdays, consider allocate the extra 13 people to 12 months. But none of these works. And I am now really confuse.

Any help would be very generous!
Thank you!

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AlephZero
Homework Helper
Start by answering the question, "what is the probability that none of the 25 people was born in January".

Then think how to use that (and similar probabilities that are easy to find) to answer the original question.

But I am still confused, because by considering none in Janurary, it also include the situation none in Feburary, none in march...etc.. (the method I use is just 11^25...) So there is repetitions.....

May you enlight me a bit more?

But I am still confused, because by considering none in Janurary, it also include the situation none in Feburary, none in march...etc.. (the method I use is just 11^25...) So there is repetitions.....

May you enlight me a bit more?
You're on the right track - since the probabilities overlap, the inclusion-exclusion principle could be applied.

There's a few other ways to do it (markov matrices, exponential generating functions) but this is probably the most intuitive.