Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
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
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?

share|cite|improve this answer
Thank You Very Much Joriki, I have a clearer picture now. – Adel Apr 10 '12 at 16:29

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.