In how many ways can 5 different keys be placed on a keychain? (Two arrangements are considered the same if one can be rotated or flipped to be identical to the other.)
+171 if we were to arrange the keys in a row it would be factorial 5, and on a circle, it would be factorial 4, but since it's on a keychain we have to divide by two
thus we get $ \frac{4!}{2} \ \ \Rightarrow \ \ \ \frac{24}{2} = 12 $ different ways.
+171 if we were to arrange the keys in a row it would be factorial 5, and on a circle, it would be factorial 4, but since it's on a keychain we have to divide by two
thus we get $ \frac{4!}{2} \ \ \Rightarrow \ \ \ \frac{24}{2} = 12 $ different ways.
