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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 15, 2020
 #1
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Well, you need to use Combinations to solve this problem. You have 6 items, and you need to choose 2. Therefore, you have \(6 \choose 2\)=15, Thus the answer is \(15\). I hope this is what you were looking for. 

 Mar 15, 2020
 #2
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Please do not post AoPS questions on this forum. I have made this mistake before, and it did not turn out well.

 Mar 15, 2020
 #3
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No, it was 30. I found this out because you can assemble the beads into 5. different ways with one bead being stationary the whole time. Then there can be 6 other ways that the stationary bead can be placed. Therefore, the answer is 5*6=30

 Mar 15, 2020

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