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In how many ways can I place 5 different beads on a bracelet if rotations and flips of the bracelet are not treated as different arrangements?

Aug 16, 2019

#1
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Hi Guest You can assume that the bracelet only has 5 spot because the problem didn't say anything about the length.

Then, you think hm. How many ways can I put the first bead into the bracelet?

Well because we have 5 beads there are 5 choices.

Next, you think after you put the first bead how many choices are there to put the second bead into the bracelet?

Because you already put one bead into the bracelet, there are only 4 choices.

You find that the patatern is 5, then 4, then 3, then 2, then finally 1 final choice.

Multiply them all together you get 120. Notice that $$120 = 5!$$

But since rotations and flips are not the same, you have to divide by 5, $$\frac{120}{5}=24$$

then you divide by 2 because flips aren't the same so the answer is $$\boxed{12}$$

-From Evan Aug 16, 2019
edited by EvanWei123  Aug 16, 2019
#3
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No problem :D

Aug 16, 2019