Calculate the number of different necklace combinations given 3 yellow, 2 red, and 1 blue.


I get a fraction as an answer and I don't think that is right.
I think I am having the most trouble with the rotations.

Work so far"

Identity element: 1 element of that type and 60 elements fixed

180: 1 element of that type and 0 fixed

120/240: 2 element of that type and 2 fixed

60/300: 2 element of that type and 2 fixed

flip between: 3 element of that type and 0 fixed

flip across bisection: 3 element of that type and 2 fixed



so then i get (1*20 + 1*0 + 2*2 + 2*2 + 3*0 + 3*2)/12 = 74/12