Multiple properties and property combinations

[FirstInLine]

Here's something I know there must be a way to easily figure out... but not by me!

THE QUESTION...
if I have x number of categories to choose from, how many combinations can I get?

for example I think that if I had 4 categories there are 15 possible combinations

categories A, B, C, D

combinations:
A
B
C
D
AB
AC
AD
ABC
ABCD
BC
BCD
CD
ACD
ABD
BD

Am I missing any?

so if 4 yeilds 15

5 yields ?
6 yields ?

I'm know a pattern develops but how does it work? Sorry I've been out of school for so long and I don't know where to begin.

 

[mathman]

The number of subsets, of a finite set with n members, is 2ⁿ including the empty set. Omiting the empty set leaves 2ⁿ-1, which is what you got.

 

[FirstInLine]

Thanks Mathman. I knew it was some sort of sequence - 1. I just can't remember all that math I used to be so good at. Maybe I should dig up some old notes and give my brain a workout with a refresher. Hell I can't even remember my simple trig anymore