SOLUTION: how many necklaces can be made from 6 beads of different colors? the answer is 60, but how?

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Question 883539: how many necklaces can be made from 6 beads of different colors?
the answer is 60, but how?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
There are 6 beads in that necklace and each one is a different color.
Identify the colors by the codes 1, 2, 3, 4, 5, and 6.
Lay the necklace on the table and look for the bead of color 6.
What are the other colors read clockwise from that bead?
Is it 12345? 15324? Some other sequence
There are 5%21=5%2A4%2A3%2A2=120 such sequences.

However, 12345 and 54321 represent the same necklace flipped over.
By laying the necklace on the table we made it easier to count the possibilities, but we counted each one twice.
There are 120%2F2=highlight%2860%29 possible necklaces.

NOTE:
Your teacher wants you to mention "permutations".
It is just one of many names/words (hopefully not too many) that they will make you learn. Words and symbols help us communicate more efficiently, as long as we use them just as necessary.