Given n objects, I can derive that the number of ways to sample (without ordering) k times with replacement is (n+k-1 choose k). But why isn't it n^k/k! = the number of ways to sample (with ordering) k times but discounting the permutations of those samples? Any simple visual way to explain this?
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closed as too localized by Andrew Stacey, Yemon Choi, Robin Chapman, Pete L. Clark, Gjergji Zaimi May 12 2010 at 9:44 |
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You are counting samples that actually contain repetitions too few times. E.g. the sample that consists of the same object has to be counted as 1 possibility and you count it as 1/k!. |
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