Original array retrieval

$\large{\text{Why not?}}$

For an array of size $S$ , filled with $S$ number of data items or entries, there are $S!$ different possible arrangements or combinations, but when they (all the combinations) are sorted in same order (either ascending or descending), they give a unique pattern. That is, there is a many-to-one relationship between an unsorted array and the sorted one, therefore we cannot retrieve the original array.

Assume an array of size $3$ containing $1$ , $2$ and $3$ at random positions, now what do you assume about the location of each of the numbers? Obviously, you have $6$ different answers, but when you are asked about the sorted array, you have two answers $(1,2,3)$ and $(3,2,1)$ . Therefore, by judging the sorted array only, we cannot get or know the original one.