For example, how many unique ways can you arrange the six letters AAABBC without counting identical arrangements? I'm not looking for an answer to this specific example, but generally how a problem like this should be approached. Is there a method to generating a formula that gives you a direct answer based on the number of duplicate items in the sample set, or is there a way to calculate just the number of duplicates to be subtracted from a simple permutation?

I don't need this for homework help of any kind. I seriously lose sleep thinking about these things ... it's in my blood. I'm not sure if it will be an easy situation to address, but if there are any resources I could be pointed to it would be greatly appreciated, either online or in a book. I plan on going to a bookstore tomorrow to see if I can find anything and may go to the library over the weekend if I don't find anything by then. Thanks for the help!