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Birthday problem with repetitions

  1. Dec 4, 2014 #1
    1. The problem statement, all variables and given/known data
    How many different sets of birthdays are available with k people and 365 days when we don’t distinguish the same
    birthdays in different orders?

    2. Relevant equations

    I approached this using what was proven in a previous problem, provided I did that right. This what I had:

    ## C_{n+k-1, k} ##

    for combinations that involve repetitions.

    3. The attempt at a solution

    ## C_{365+k-1,k} ##

    Not much of an attempt at the solution since it seemed obvious enough. But the book says the answer is ## C_{365+k,k} ## and I'm struggling to get to this solution.
     
  2. jcsd
  3. Dec 5, 2014 #2

    haruspex

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    I agree with your answer. As a check, we can consider a much simplified version: 2 days, 2 people. C2+2-1,2 = 3: (1,1), (1,2), (2,2).
     
  4. Dec 5, 2014 #3
    Thanks haruspex. You've been a great help for me so far.
     
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