How many combinations of 6 items are possible? I have 6 items and want to know how many combinations are possible in sets of any amount. (no duplicates)
e.g. It's possible to have any of the following:
1,2,3,4,5,6
1,3,5,6,2
1
1,3,4  
there cannot be duplicate combinations:
1,2,3,4
4,3,2,1
Edit: for some reason I cannot add more comments. @miracle173 is correct. Also {1,1} is not acceptable

My thought was:
Each combination of $k$ elements $n$ by $n$ can be express by  $^kC_{n}$.As I understood you want to make sets of $1,2,3,4,5$ and $6$ elements from a sample of $6$ elements without reapeting.So there is a line in pascal's triangle where $k=6$ and $n \in \{ 1,2,3,4,5,6\}$, I'll not include the $0$.
Then we'll get:
$^6C_{1}+^6C_{2}+^6C_{3}+^6C_{4}+^6C_{5}+^6C_{6}=2^6-1$
The minus $1$ is because the $^6C_{0}$ is not inclued.
I thing is that.
Explain:
Each combination refers to each set. A set of $1$ element, a set of $2$ elements...and so on.The $^6C_{0}$ it's not valid for this particular problem, because the problem don't allow the empty set. For any line of the Pascal's triangle the sum of all elements of this line is given by $2^n$, where  $n$ is the number's line.So if the $^6C_{0}$ is not inclued the solution is given by $2^n-1$, where in this case $n=6$.
