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Yvette has six beads that she is going to assemble into a bracelet. Two of the six beads have the same color, and the remaining four all have different colors. How many different ways can Yvette assemble her bracelet? (Two bracelets are considered identical if one can be rotated and/or reflected to obtain the other.)

 Mar 2, 2020
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Yvette has six beads that she is going to assemble into a bracelet. Two of the six beads have the same color R, and the remaining four all have different colors BGYP. How many different ways can Yvette assemble her bracelet? (Two bracelets are considered identical if one can be rotated and/or reflected to obtain the other.)

 

Im going to let the B mark the beginning. Now I have 5 more beads and 2 are the same.  So I think that is 5!/2! = 60 ways

 

Lets try it a different way

Let a red mark the beginning then I have 5!/2 which will still equals 60

 

So I think the answer is 60.  Oh dear I have accounted for rotation but not for reflection.

I did work out how to deal with reflection before but I have forgotten.....

 

So the answer is less than 60. 

I think Just divide by 2

So my best guess is that the answer is 30

 

Let us know when you find out the given answer.

 Mar 2, 2020

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