# Permutations from a set

Part of my problem is I can't figure out which question answers my problem. I'm not so familiar with the kind of math lingo that I know how to ask this question, so I'm gonna bumble my way through this as best I can.

I have a set of 24 words - I'm trying to come up with all possible 'combinations' (permutations?) of the set - it can have as many as 24 words in it, but it has to have at least 2, and I want to cut out duplicates. So say it has the words 'jump' and 'fall' in it - jump - fall would be a combination, but for all intents and purposes for my list, fall - jump is the same combination, and I don't want it counted twice. If someone can just point me in the right direction, or just tell me what it is I'm even looking for...

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I assume you want to choose $2$ to $24$ words from the $24$ available.

Line up the words in a row, and go down the row from left to right, writing a $Y$ if you want to use the word, and a $N$ if you don't.

At each word, you have $2$ choices. So the total number of possible choices is $2^{24}$.

However, these choices include the $NNN\dots N$ possibility, which is forbidden, and also the choices where you write $Y$ for exactly one word, and $N$ for the others. There is $1$ way to say $N$ to every word, and there are $24$ ways to say $Y$ to a single word, and $N$ to all the others, for a total of $25$.

Thus the required number is $2^{24}-25$.

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Now that you've said it in a way that's been dumbed down to my level, I understand it. Thank you! –  Jack Jan 17 '14 at 3:59
You are welcome. It was not dumbing down, it is the way I think about these things, very concretely. –  André Nicolas Jan 17 '14 at 17:01