Question 94
The faces of a numbered die are to be painted by 6 distinct colours: Red, blue, green, black, indigo, and violet. In how many ways can the faces be painted such that the red, green and blue faces share a corner of the cube?
Solution
There are eight corners in the die; we can choose any of them in 8 ways.
Say we choose the corner with numbers (3,5,1); now we have to paint them in colours red, blue and green.
This again can be done in 3! ways.
The remaining three faces are to be painted with the remaining three colours, which again can be done in three ways!
Giving us a total of $$8\times\ 6\times\ 6=288$$
Therefore, Option E is the correct answer.
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