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How many permutations?

  1. Jan 25, 2010 #1
    this problem has been on my mind...

    how many permutations can you make with 30 'A's and 30 'B's

    or rather the same question, how many unique numbers can be made from 30 1s and 30 0s

    any ideas?
    (excluding permutations that look identical)

    thanks
     
  2. jcsd
  3. Jan 25, 2010 #2
    Use permutations with repetition.
     
  4. Jan 25, 2010 #3
    it might be 60! / (30! x 30!)
     
  5. Jan 25, 2010 #4
    It is.
     
  6. Jan 25, 2010 #5
    In general if we have say a sequence of n items and say k objects/elements are repeated s_j times correspondingly j=1,2,...,k, then the total nr. of permutations is:

    n!/[(s_1)!*..*(s_k)!]
     
  7. Jan 25, 2010 #6
    Here is another way to look at the problem.

    You have a sequence of 60 symbols; you choose 30 of them to be A's. (The others will be B's.) This can be done in
    [tex]\binom{60}{30}[/tex]
    ways.
     
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