Mathematics - Permutation & Combination Question with Solution | TestHub

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)

$\text{ ∴ Ans }=5\times (4-1)!=30\text{ ways. }$