You have a six-sided cube and six cans of paint, each a different color. You may not mix colors of paint. How many distinct ways can you paint the cube using a different color for each side? (If you can reorient a cube to look like another cube, then the two cubes are not distinct.)
(A) 24
(B) 30
(C) 48
(D) 60
(E) 120
OA:B
we can choose top of the cube in 6 ways. lets fix this point and then we can choose 5 different colors for the bottom B. as A is fix so we have 5 ways to choose bottom. the other 4 faces are in circular way and thus we have (1/4) (4!) = 6 ways to color it. in total we can color the cube in 5.6 = 30 ways.
this question is easy to do but my concern is what if we change the condition from non-distinct to distinct cubes??? what will be the answer then?
(A) 24
(B) 30
(C) 48
(D) 60
(E) 120
OA:B
we can choose top of the cube in 6 ways. lets fix this point and then we can choose 5 different colors for the bottom B. as A is fix so we have 5 ways to choose bottom. the other 4 faces are in circular way and thus we have (1/4) (4!) = 6 ways to color it. in total we can color the cube in 5.6 = 30 ways.
this question is easy to do but my concern is what if we change the condition from non-distinct to distinct cubes??? what will be the answer then?
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