Child’s Play Puzzle

Child’s Play Puzzle. The game played by children a puzzle for others.

A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you press the start button and fit the tetrahedron into the triangular hollow or the cube into the square hollow it rings a bell.
It only rings the bell again if you then fit the tetrahedron or the cube into its hollow in a different way from any you have done before. It plays one tune when you have fitted the tetrahedron into its hollow in all the ways possible and another tune when you have fitted the cube into its hollow in all the ways possible.
This completes the game. How many times does the bell ring in a complete game?
Now suppose a similar toy is made involving all five platonic solids. How many times does the bell ring in a complete 5-solid game?

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