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...


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 $2^{24}-25$.

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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