Hello, bm203!

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 mosttwo matching numbers?

(b)at leasttwo 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 dowant 3 matching numbers.not

. . There are: ways to have 3 matching numbers.

Hence, there are: . ways to have at most 2 matching numbers.

Therefore: .

(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.

. .

Therefore: .