# How do I approach this combinatorics problem involving labeled and unlabelled configurations

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

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