Question

The no of ways of painting the faces of a cube of six different colours is :
a)1
b)6
c)6!
d)36

How ?

Answer 1

I think you need to take into account that two colored cubes are considered equal if you can rotate one and make it look like the other one. If that were not the case, the answer would be 6!.

Answer 2

Decide that the face with color 1 is facing you. The other five faces can be colored in 5! ways, but for each such coloring there are precisely three duplicates. You can see this by rotating the cube around the axis of the face facing you. To remove the duplicates, you need to divide by 4. Final answer: 5!/4 = 120/4 = 30.

But that's not in the list...

Answer 3

Oh right, there could be even more duplicates, but we know now that there are 30 possible colorings _or less_, leaving only a and b as possible answers. There is more than one way (one is when color 1 and 2 are opposite and another is when they are not), so the only answer left is b.

Answer 4

Thanks for helping , but the answers seems to be 1. And I don't know how :(

Answer 5

it is d because since there are 6 faces, each color would be painted.If you do 6 times 6 it would give you 36 ways.

Answer 6

each face would have 6 colors and there are 6 faces

Answer 7

A cube had six faces. Each face will have only one possibility of getting a color.

Answer 8

no there are 6 ways for each face so 6 times 6 =36
6(6)=36

Answer 9

it is D