In how many ways can I combine x elements

Question

In how many ways can I combine x elements and why?
Example: If I have 6 elements, indicating each element with a number, some possible cases could be: $1,2,3/\,1,4,3/\, 1,2,5,6/\, ...$

Answer 1

You are looking for,

$xC_0+xC_1+\dots+xC_x=2^x$