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.

Use binary!
1, 2, 4, 8, 16 adds up to 31

The number of combinations with 6 numbers would be 63

Seven digits would be 127, etc. 
