What is the total number of combinations of 5 items together when there are no duplicates? I have 5 categories - A, B, C, D & E.
I want to basically create groups that reflect every single combination of these categories without there being duplicates.
So groups would look like this:


*

*A

*B

*C

*D

*E

*A, B

*A, C

*A, D

*A, E

*B, C

*B, D

*B, E

*C, D
.
.
.
etc.


This sounds like something I would use the binomial coefficient $n \choose r$ for, but I am quite fuzzy on calculus and can't remember exactly how to do this.
Any help would be appreciated.
Thanks.

Think about this from another angle. You want some number of these five categories without repetition.
Well each category is either chosen by you or not chosen by you. Each such choice bears no relationship with the other choices.
Thus there are $2^5 = 32$ possibilities. However, you are not counting the choice of none of the five categories, so we subtract $1$ to get $31$ possibilities.
