Why does Python’s itertools.permutations contain duplicates? (When the original list has duplicates)

It is universally agreed that a list of n distinct symbols has n! permutations. However, when the symbols are not distinct, the most common convention, in mathematics and elsewhere, seems to be to count only distinct permutations. Thus the permutations of the list [1, 1, 2] are usually considered to be
[1, 1, 2], [1, 2, 1], [2, 1, 1]. Indeed, the following C++ code prints precisely those three: