Question
In how many different ways can the six faces of cube be painted by 6 different colours?
Answer: Option C
:
C
Mark a particular face X. (Later on, we will have to divide whatever answer we get by 6 because all 6 faces are identical at this point, and we have chosen one out of 6 randomly).
Put a colour on face X. There are 6 ways to do this.
Put another colour on the face opposite X. There are 5 ways to do this.
Arrange the remaining 4 colours in the remaining four places - there are 3! ways to do this (circular permutation of 4 colours = (4-1)!
Total =[(6×5×3!)]6= 30
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:
C
Mark a particular face X. (Later on, we will have to divide whatever answer we get by 6 because all 6 faces are identical at this point, and we have chosen one out of 6 randomly).
Put a colour on face X. There are 6 ways to do this.
Put another colour on the face opposite X. There are 5 ways to do this.
Arrange the remaining 4 colours in the remaining four places - there are 3! ways to do this (circular permutation of 4 colours = (4-1)!
Total =[(6×5×3!)]6= 30
Was this answer helpful ?
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