Question

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

Answer 1

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.