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counting and probability intermediate

Problem

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.)
Solution
There are ways to place the keys on the keychain, but we must divide by 5 for rotational symmetry (5 rotations for each arrangement), and by 2 for reflectional symmetry (we can flip the keychain to get the same arrangement). The answer is .
Final answer
12