A toy manufacturer makes a key ring toy with 7 different colored plastic keys. If the keys are arranged on the key ring at random, how many different key rings can be sold? Be sure to explain.

Question

anonymous · Answer

I thougt that too, but the answer sheet says 720... its just that I have no idea how to get there.

anonymous · Answer

>.<

anonymous · Answer

The sheet is wrong >:(

anonymous · Answer

it wont be 7! rather it will be 6!because in a ring there is no starting or end point

kinggeorge · Answer

It should be $6!=720$ since it's on a ring. If you were to lay out the ring as if it were a line, $7!$ would be correct, but you can rotate a ring around so the answer should be $${7! \over 7}=6!=720$$

anonymous · Answer

OH!!! Circular permutations?

kinggeorge · Answer

You have $7!$ ways of laying out the keys, but there are seven different rotations that are the same thing, so you have to divide by 7.

Circular permutations. Exactly.

anonymous · Answer

OH!!! [Impressed] Thank You guys so MUCH!!! Hey look out for my next question, k? I ll have it up in a second