You have \(4\) different colors, and you wish to paint the \(4\) faces of a regular tetrahedron, each in a different color. How many **different** ways can you do it?

**Note**: Different implies that for two coloring combinations \(A\) and \(B\), you can't pick up \(A\) and reorient it to make it look exactly like \(B\).

**Image credit:** http://www.korthalsaltes.com/

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