Back to permutations. Here is a definition:
When they refer to permutations, statisticians use a specific terminology. They describe permutations as n distinct objects taken r at a time. in the case of flags, you would have to say
3 distinct objects taken 3 at a time. Then 6 is the correct answer.
But one has to explicitly say what is ' n ' and what is ' r '. Because ' r ' = something different than 3 would give a different answer.
Translation: n refers to the number of objects from which the permutation is formed; and r refers to the number of objects used to form the permutation.
Computing the number of permutations. The number of permutations of n objects taken r at a time is
nPr = n(n  1)(n  2) ... (n  r + 1) = n! / (n  r)!
I like to keep things simple. For people like myself. But at times, lengthy essays are used to hide, waffle, distort or confuse simple people.
Check the definition of permutations in the sentence at the top. Compare it with what and how ' permutations ' were defined and used the first time the word ' permutation ' was used.
One has to define precisely the issue. There is no place for waffle.
The above definition was taken with a Google search from stattrek.com
But if repitition is allowed..that becomes a different ball game. That is why I have stressed the two conditions be met in a previous post. That makes it complete. The word ' distinct '. Blue, white, blue e.g fails my second condition. Though it is distinct.
