JEE Main Mathematics question

The number of ways of painting the faces of a cube with six different colours is

(A)
(B)
(C)
(D)None of theseCorrect

Answer: (D)

Solution

If the colourings are regarded as the same when one can be turned into the other by a rotation of the cube, fix one colour on the bottom face; the top face has choices. The four side faces then take the remaining colours in a circle in ways, so there are distinct colourings

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Question ID VK-020795