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Firstly, thank you for looking at my question.

I would like to know what this kind of problem is called in mathematics:

Given a set of letters, find all possible 'words' you can make with those letters. For example for 'abc' the solution would be:

a, b, c, ab, ac, abc, ba, bac, bca, ca, cab, cba

Some background, I am writing a computer program to play Scrabble and need to generate all possible words given from a set of letters. I'm researching algorithms for this problem but couldn't quite figure out what the general name is for this type of problem. I'm curious to find out so I thought I would ask.

I thought this was a type of permutation problem but reading up on Permutations I see that the length of the result is set, not variable. And it's not a Combination since the order matters.

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    The essential thing is not the name, but the exact definition of acceptable words (e.g., whether a word may contain the same letters more than once) and which "combinations" of letters count as the same word.2012-10-22

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The problem is about permutations of k-order. You can read about this kind of problems in the book "Discrete Mathematics and Its Applications" (Kenneth Rosen)

Regards!.

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All possible outcomes of a probability problem are called the "sample space". Is that what you were looking for?