How many bracelets can be made by putting six different-coloured beads on a ring if 10 different colours are available?The Problem:

Since there are 10 possible options and you must arrange six of the colours at a time to form a bracelet, I thought I should just use the permutation formula.Attempted Solution:

10 subscript P subscript 6 = 151 200

Since I bracelet may be fliped over, I then divided the answer by 2 to obtain 75 600.

But the correct answer is 12 600.

I am perplexed by how this could be. Could someone please help?

Note: Sorry for puting "subscript". I'm not a master of this forum's codes.