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Here is the question:

If we allow f(n) and g(n) to represent the number of labeled and unlabelled configurations, respectively, of n objects, then why is the following reasonable? You should include your assumptions (e.g., how you understand the terms “labeled” and “unlabelled”).
f(n)/n! ≤ g(n) ≤ f(n)

I appreciate any tips or advice.

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Given any unlabeled configuration using $n$ objects, there are $n!$ ways to apply labels to the individual objects. –  Austin Mohr Apr 10 '12 at 16:22
    
@AustinMohr - Thanks a lot, Cool yes that is a big hint. –  Adel Apr 10 '12 at 16:24
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1 Answer

up vote 1 down vote accepted

If you take an unlabeled configuration, in how many ways can you apply labels to the objects? What happens if these are all identical? What happens if they're all distinct?

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Thank You Very Much Joriki, I have a clearer picture now. –  Adel Apr 10 '12 at 16:29
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