2^8 is not correct.
2^8 assumes a necklace like:
is different than a necklace like:
You need to reflect this in your counting to obtain the correct (i.e. lower) answer.
This is a very tricky problem . . .
You're making a necklace with 4 red pieces and 4 yellow pieces.
How many different combination of necklaces can you make?
is 2^8 correct? . . . . no
Your answer assumes there are at least eight of each color
. . and includes all the combinations from
Even worse, this is a necklace . . . a circular arrangement.
So that, for example: .
. . That is: . . .
There is one more "trap" in a Necklace Problem, overlooked by the best of us.
This is similar to seating 4 men and 4 women around a circilar table,
. . except a necklace can be "flipped over".
So that: . . .
Care to try again?