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Joanna has seven beads that she wants to assemble into a bracelet. Three of the beads have the same color, and the other four all have different colors. In how many different ways can Joanna assemble her bracelet? (Two bracelets are considered identical if one can be rotated and/or reflected to obtain the other.)

 Jun 23, 2024
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This question is really just how to arrange the letters aaabbbb, a the first color, b the second, then dividing by 7 to get rid of the overcount. there are \(\frac{7!}{4!*3!}\) ways to do that or 35 ways. then we need to divide by 7 to deal with the overcount. so \(\boxed{5}\) ways to assemble the bracelet. >:)

 Jun 23, 2024

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