Painting A Cube

If you wish to paint the 6 faces of a cube using 6 colors, with each face in one distinct color, how many different ways can you do it?

Clarification: 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: Puzzles.com
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