A string of beads is made up of 5 orange and 5 black beads. If they are randomly arranged around the necklace, how many possible combinations are there?
These questions always get me. Anyway thanks to anyone who helps
review permutations with duplicates.
10!/(5!5!)
That is, for each of the 10! permutations, the 5 beads of the same color cannot be distinguished, so you need to divide by the 5! ways they can be shuffled about.
Of course, permutations in a circle are a little more involved, but I assume we can open the clasp of the necklace and lay it out flat.