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Combination with repeatation formula

  1. Jun 2, 2015 #1
    1. The problem statement, all variables and given/known data
    The combination of n different object, taken r at a time(repeatation allowed) is given by
    Cnr = (n-1+r)! / [(n-1)! r!]


    2. Relevant equations


    3. The attempt at a solution
    The above formula is deducted, as it is same as no. of ways of placing n-1 bar in n-1+r places, which is same as combination (repeatation not allowed) of n-1 object placed in n-1+r places. But permutation and combination formula or online calculator doesn't allow when r>n, (r= place, n= no. of objects). Then how is the prove of the above formula deducted?

    Also the above formula is similar to combination(repeatation not allowed) of n-1+r object placed in r places.
     
  2. jcsd
  3. Jun 4, 2015 #2

    haruspex

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    "At a time" should not be used when describing combinations that allow repetition. See e.g. http://en.wikipedia.org/wiki/Combination.
    Does your calculator have separate functions for with and without repetition? If it does, you must be selecting the wrong one. If it does not, you must do the n+r-1 calculation separately and plug that into the function as 'n'.
     
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