Question 95
Cecilia has a six-faced die (numbered from 1 to 6) and 4 colours at her disposal. In how many ways can she colour the six faces of the die using in total at least three different colours and making sure that opposite faces have different colours?
(A) $4^{3} \cdot 3^{3}$
(B) $3^{6}-2^{6}$
(C) $2^{6} \cdot 3^{2}$
(D) $2^{4} \cdot 3 \cdot 5 \cdot 7$
(E) None of the above
(A) $4^{3} \cdot 3^{3}$
(B) $3^{6}-2^{6}$
(C) $2^{6} \cdot 3^{2}$
(D) $2^{4} \cdot 3 \cdot 5 \cdot 7$
(E) None of the above