$3$ dice are thrown simultaneously

$3$ dice are thrown simultaneously

I have a doubt in this question:
Three dice are thrown simultaneously. Find the probability that:
All show distinct faces
Two of them show the same face
My approach is for 1): $$
\frac{_6C_1}{_6C_1}\cdot\frac{_5C_1}{_6C_1}\cdot\frac{_4C_1}{_6C_1}\cdot
3! $$ and for 2): $$
\frac{_6C_1}{_6C_1}\cdot\frac{1}{_6C_1}\cdot\frac{_5C_1}{_6C_1}\cdot\frac{3!}{2!}
$$ but the correct solution is for 1): $$
\frac{_6C_1}{_6C_1}\cdot\frac{_5C_1}{_6C_1}\cdot\frac{_4C_1}{_6C_1} $$ and
for 2): $$
\frac{_6C_1}{_6C_1}\cdot\frac{1}{_6C_1}\cdot\frac{_5C_1}{_6C_1}\cdot\frac{3!}{2!}
$$