In each case, calculating the permutation isproceeds by using the leftmost factoradic digit (here, 0, 1, or 2) as the first permutation digit, then removing it from the list of choices (0, 1, and 2). Think of this new list of choices as zero indexed, and use each successive factoradic digit to choose from its remaining elements. If the second factoradic digit is "0" then the first element of the list is selected for the second permutation digit and is then removed from the list. Similarly, if the second factoradic digit is "1", the second is selected and then removed. The final factoradic digit is always "0", and since the list now contains only one element, it is selected as the last permutation digit.
The process may become clearer with a longer example. Let's say we want the 2982nd permutation of the numbers 0 through 6. 2982 is 4041000<sub>!</sub> in factoradic, and that number picks out digits (4,0,6,2,1,3,5) in turn, via indexing a dwindling symbol set:
