I'm trying to understand this problem as exposed in William Feller's An introduction to probability theory and its applications:
(d) Flags of one or two colors. In example (1.f) it was shown that r flags can be displayed on n poles in N = n(n+ 1) ... (n+r-1) different ways. We now consider the same problem for flags of one color (considered indistinguishable). Numbering the flags of such a display yields exactly r! displays of r distinguishable flags and hence r flags of the same color can be displayed in N/r! ways.
I understand that a group of r distinguishable elements yield r! ordered samples of size r. But I do not understand why is it that r undistinguished flags can be displayed in N/r! ways. As I think about it, since they are supposed to be undistinguished, shouldn't there be only one way to order them? Does N/r! always yield 1? If so, why?