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Permutation with exception/repetition

  1. Dec 3, 2015 #1
    I need a formula to calculate permutation.
    For example I have a 5 numbers and I creating a 3 digit number from it.
    The numbers are: 1, 1, 1, 2, 3; I could write up 13 variations, but I couldn't work out the formula.
    If the numbers are: 1, 1, 2, 2, 3 the number of variations are 18 (if I wrote them up properly)
    Is there a formula to calculate this, or is it becoming too complex?
  2. jcsd
  3. Dec 3, 2015 #2
    You're looking for permutations of a multiset (a set in which redundant elements are allowed).
    (See https://en.wikipedia.org/wiki/Permutation#Permutations_of_multisets.)
  4. Dec 3, 2015 #3
    Thanks. It is almost what I need except in those example they use up all element of each set.
    I would only use part of it. So if the sets are {1, 1}{2, 2}{3} then I have a total of 5 elements. And the question is how many different 3 digit numbers I can create of these 5 elements. Because they are numbers, the order matter so it would be a kind of permutation.
    What would be the formula for that?
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