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Math Help - birthday problem

  1. #1
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    Lightbulb birthday problem

    Given 20 people, what is the probability that among the 12 months in the year there are 4 months containing exactly 2 birthdays and 4 containing exactly three birthdays.

    I'm able to proceed as far as computing the sample space which is 12^20, but no further. Can some one shed some light on the number of required outcomes?
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  2. #2
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    Re: birthday problem

    Here is an approach that may work. Maybe you can answer these questions:

    1. There are three types of months: those with no birthdays (4 of them), those with 2 birthdays (4 of them), and those with 3 birthdays (4 of them). How many ways can you assign months to those three classes?
    2. Given an assignment of months to those classes, in how many ways can 20 people be assigned to the months?
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  3. #3
    MHF Contributor matheagle's Avatar
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    Re: birthday problem

    not sure if this helps
    but today is my birthday
    probably not
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  4. #4
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    Re: birthday problem

    Matheagle,

    I think I am a day late, but nonetheless, I hope you have (had?) a Very Happy Birthday.
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