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    <p>"<a href="http://en.wikipedia.org/wiki/Generating_function" rel="nofollow noreferrer">Generating Functions</a>" comes to mind as one construct that can be used when solving this type of problem. I'd note that there are several different generating functions depending on what you want.</p> <p>In North America, car license plates can be an interesting combinatorial problem in counting all the permutations where there are 36 possible values for each place of the 6 or 7 that are the lengths of license plates depending on where one is getting a plate. However, some combinations are disqualified due to there being swear words or racist words in some of them that makes for a slightly harder problem. For example, there is an infamour N-word that has at least a couple of different spellings that wouldn't be allowed on license plates I'd think.</p> <p>Another example would be determining all the different orders of words using a given alphabet that contains some items repeated multiple times. For example, if one wanted all the different ways to arrange the letters of say the word "letter" it isn't just 6! which would be the case of "abcdef" because there are 2 pairs of letters that make it slightly trickier to compute.</p> <p><a href="http://en.wikipedia.org/wiki/Leet" rel="nofollow noreferrer">L33t</a> can be another way to bring in more complexity in identifying inappropriate words as while a-s-s gets censored a$$ or @ss may not necessarily be treated the same way even though it is basically the same term expressed in different ways. I'm not sure if many special characters like $ or @ would appear on license plates but one could think of parental controls on web content as having to have these kinds of algorithms to identify which terms to censor.</p>
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    1. COThe "letter" problem isn't difficult to compute. It's basically n!/(l!e!t!r!). In the more general case, divide the factorial of the number of letters by the product of the factorials of the numbers of each individual letter.
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