Your second answer is correct; your first answer is off.
Let me show you a way to avoid making long lists . . .
If three (fair) dice are rolled what is the probability of rolling:
(a) at most two matching numbers?
(b) at least two matching numbers?
There are: . possible outcomes.
(a) At most two matching numbers. .This means 0 matching numbers,
. . .1 matching number (whatever that means?!), or 2 matching numbers.
We do not want 3 matching numbers.
. . There are: ways to have 3 matching numbers.
Hence, there are: . ways to have at most 2 matching numbers.
(b) At least 2 matching numbers.
. . .This means: 2 matches or 3 matches.
For 2 matches, there are 6 choices of for the value of the Pair.
We want: in some order.
For 3 matches: there are 6 choices for the value of the Triple.