I don't understand why the solution to this probability question is set up in this manner The problem states: A pair of dice is cast until either the sum of seven or eight appears.
(a) Show that the probability of a seven before an eight is 6/11.
(b) Next, this pair of dice is cast until a seven appears twice or until each of a six and eight have appeared at least once. Show that the probability of the six and eight occurring before two sevens is 0.546.
I understand part (a). For part (b), I was reading the following solution:

I don't understand why we can say, "we will only consider rolls where a 6, 7, or 8 are rolled." That does not seem to include every case. For instance, what about the case where we have 668, 886, or 6677?

In essence, you only need to consider rolls that matter.
Rolls other than $6,7,8$ don't matter ever in this problem.
Rolling $6$ again after you've already gotten a $6$ doesn't matter either, because you've already satisfied rolling $6$ "at least once."  At this point, rolling another $6$ matters as much as rolling an $11$.
Same with rolling two $8$'s (or three, or seventeen).
