You have a six-sided cube and six cans of paint, each a different color. You may not mix colors of paint. How many distinct ways can you paint the cube using a different color for each side? (If you can reorient a cube to look like another cube, then the two cubes are not distinct.)
Choices: A) 24 B) 30 C) 48 D) 60 E) 120
Paint one of the faces red and make it the top face.   5 options for the bottom face.   Now, four side faces can be painted in   (4-1)= 
<gadget id="calculator">  (4-1)</gadget>
<output>3</output>
3!= 6 ways (circular arrangements of 4 colors).   Total = 5*6= 
<gadget id="calculator">5*6</gadget>
<output>30</output>
30.   Answer: 30.
<result>B</result>
You have a six-sided cube and six cans of paint, each a different color. You may not mix colors of paint. How many distinct ways can you paint the cube using a different color for each side? (If you can reorient a cube to look like another cube, then the two cubes are not distinct.)