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How many different bracelets have 3 identical orange beads, 3 identical black beads, and 1 teal bead, if rotating or flipping a bracelet does not change it?


Is the answer 720 or 140? I have no idea

 Nov 18, 2018

I think it is only 10 ways.


Put the teal bead on first. It is the marker bead. This takes care of the rotation aspect.

Then you have 2 lots of 3 identical beads. so that is 6!/(3!3!) ways to place them. Which is 20 ways.

But the braclet can be flipped so I think this will halve the number of possibilities

For instance  TOOOBBB is the same as TBBBOOO

So I think the answer is 10 ways.

 Nov 18, 2018

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