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What is the probabilty that there are no 2 people's in 12 people room with the same birthday month ?

I thought about $\frac{12!}{12^{12}}$,but , i think its wrong. What do you think ?

Thanks.

NM2
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    i think it's correct. $P($ all people have different month of birth $) =$$\frac{12!}{12^{12}}$ – K.K.McDonald Mar 28 '16 at 20:54
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    It's correct, if you make the simplifying assumption that each month has an equal probability. – lulu Mar 28 '16 at 20:57
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    This was asked a few days ago. See http://math.stackexchange.com/questions/1713324/the-probability-that-no-person-has-the-same-birthday-month?rq=1 – Barry Cipra Mar 28 '16 at 21:05
  • https://math.stackexchange.com/questions/1475378/what-is-the-probability-that-nobody-is-born-in-the-same-month?rq=1 – PatrickT Apr 02 '18 at 17:42

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