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Khaled has a cube in his hand and takes it to a painter who has 6 different colors. He asks the painter to color the cube so that each face has a different color. In how many ways can this be done?

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Answer to a math question Khaled has a cube in his hand and takes it to a painter who has 6 different colors. He asks the painter to color the cube so that each face has a different color. In how many ways can this be done?

Expert avatar
Miles
4.9
114 Answers
1. Calculate the total number of permutations of the 6 colors:
6! = 720

2. Account for the rotational symmetries of the cube (24):
\frac{720}{24} = 30

The final answer: 30 ways to paint the cube with each face a different color considering the cube's rotational symmetries.

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