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Puzzle | Six colored cube

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Given six distinct colors, in how many unique ways can a six faced cube be painted such that no two faces have the same color? Note: Mixing of colors is not allowed. Answer: 30 ways Explanation: To avoid repetitions, let us fix the color of the top face. Hence, the bottom face can be painted in 5 ways. Now, what remains is the circular arrangement of the remaining four colors which can be done in (4-1)! = 3! = 6 ways (For n distinct objects, number of distinct circular arrangements are (n-1)!). Hence, the answer is 5*6 = 30 ways.

Last Updated : 18 Jan, 2023
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