binary+counting+for+all+possible+combinations+of+elements

If there are several elements which can be either included or not included to form a group, then all possible groups can be generated by simply counting in binary from 1 to 2^(# of elements).

One way of doing this could be to use excel. Let's say we have 3 elements. In excel we would count from 1 to 8. Then we would convert these numbers to binary (DEC2BIN function). Then we could put the leading 0s in front of these binary elements by repasting the numbers so they don't include any formulas then format cells->custom->000#. These numbers could be turned into a matrix if desired by using a regex to f (\d) r $1\t

Then headers could be placed at the top of each column. The final result might look something like this.


 * || element 1 || element 2 || element 3 ||
 * 0 || 0 || 0 || 1 ||
 * 0 || 0 || 1 || 0 ||
 * 0 || 0 || 1 || 1 ||
 * 0 || 1 || 0 || 0 ||
 * 0 || 1 || 0 || 1 ||
 * 0 || 1 || 1 || 0 ||
 * 0 || 1 || 1 || 1 ||
 * 1 || 0 || 0 || 0 ||