Suppose you have a set of 4 elements {A,B,C,D}, but without specifying their order. Now, if you want to specify which precedes which, that would mean you need to provide more information.
But at the same time, writing down the ordered list {B,C,A,D} doesn't take more text. That's probably because order is implicit when writing down things, even when I say that {A,B,C,D} is unordered, the way I write it down has order, I just tell you to ignore it.
So which is true? Does order carry additional information, and if so, why don't ordered lists take more text to describe than unordered ones?