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

Your are asking the number of subsets of a set with n elements.{1,2,3,...,n}
Each subset can be represented by a binary string, e.g for the set {1,2,3,4,5,6} the string 001101 means the subset that
does not contain the element 1 of the set, because the 1st left character of the string is 0
does not contain the element 2 of the set, because the 2nd left character of the string is 0
does contain the element 3 of the set, because the 3rd left character of the string is 1
does contain the element 4 of the set, because the 4th left character of the string is 1
does not contain the element 5 of the set, because the 5th left character of the string is 0
does contain the element 6 of the set, because the 6th left character of the string is 1
so 001101 means the subset {3,4,6}. Therefore there asre as many subsets as strings of length n. With n binary digits one can count from 0 to 2^n-1, therefore there are 2^n such strings and 2^n subsets of {1,....,n}. 00...0 means the empty subset. if you dont want count the empty subset then you have only 2^n-1 subsets.
