In how many ways can a cube be colored by 6 six different colors such that each face has a different color?

Question

Answer is not :-
6 , 5, 6^6 , 6! , (6!)^2 , 5!

Answer 1

1 ?

Answer 2

Assuming that we shouldn't count cubes that could be rotated to be the same as other cubes:

* Apply any color to the top: 1 choice
* Apply a different color to the bottom: 5 choices
* Apply any color to the front: 1 choice (any color can be rotated to the front)
* Apply a color to the left: 3 choices
* Apply a color to the back: 2 choices
* Apply a color to the right: 1 choice.

Answer: 5*3*2 = 30

Answer 3

Think of a Rubic's cube. It is a cube with 6 colors. It has 6 surfaces. 6*6 = 36

Edit: I'm still trying to understand why there is a concern about 2 cubes being the same color. How can that happen if there are 6 colors and only 6 sides? I guess I'll have to get me a cube and try it out!!!

Answer 4

Top and bottom can be painted by 2 out of 6 colors in 6x5 = 30 ways.
Sides can be painted with remaining 4 colors in 4!/2 ways = 12 ways.
Total no. of ways = 30 x 12 = 360.

Answer 5

wel equal oppo. is right i have studied this subject its probablity so probablity of colors is 6
probability of surfaces is is 6 also
6 x 6 = 36 but then we substract the probability of the cubes surface being colored by the same color each times so
36 - 6 = 30 im absolutly right

Answer 6

use ncx
6c6= 6*1+6*2+6*3+6*4+6*5+6*6
6+12+18+24+30+36
= 126

cube has 6 sides and they have given six colors
eg you have 3 number and 3 color red,blue and green
1 2 3
red blue green
red green blue
blue red green
blue green red
green red blue
green blue red

total is 18ways
3*1+3*2+3*3
3+ 6+　9 = 18

Answer 7

like a Rubic's Cube?