Question

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

• A. 1
• B. 720
• C. 30
• D. 15

Answer 1

The correct option is C 30

First paint any colour on any face. Now the opposite face can be painted in 5 ways (with anyone of the remaining 5 colours). Now, the remaining 4 faces can be painted with the remaining 4 colours in (4-1)! ways. (circular permutations)
$\therefore$ Ans =$5\times (4-1)!=30ways$.