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Q.

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


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a

30

b

6

c

6!

d

None of these. 

answer is A.

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Detailed Solution

It is known that,
Total sides of a cube = 6
Goiven,
Total colour on 6 cube faces= 6
Now let the below face of cube is painted with a colour. So, the top face can be painted by 5 ways with 5 different colours.
Now from the cicular permutation concept, the remaining side faces can be painted by 4 colours in (4-1)! Ways.
Thus, the total number of ways,
=5×4-1!
=5×3×2 
=30 Ways   So, there are total 30 required ways.
Correct option is 1.
 
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