When do repeats count separately in probability?

[yo4561]

I was watching Jeff's Free GMAT Prep Hour video on probability.

He shows this following problem: If you roll two standard, six-sided dice, what is the probability that the product of the two numbers facing up is even?

He then does:
Even and Odd
Odd and Even
Even and Even

I am confused on why you wouldn't also count even and even again? In other words:
Even and Odd
Odd and Even
Even and Even
Even and Even

I understand that it is repetitive, but couldn't you argue it's repetitive to have "even and odd" then "odd and even"? Thank you!!

[esledge]

I understand that it is repetitive, but couldn't you argue it's repetitive to have "even and odd" then "odd and even"? Thank you!!

"Even and then Odd" actually is different from "Odd and then Even," though, whereas the list of "Even and then Even" scenarios already contains the list of the scenarios of the reversed order.

To really see this, try one or both of these exercises:
(1) list out all 36 possible die outcomes, and count the EO, the OEs, and the EEs.
(2) Draw a decision tree (first branching is the 1,2,3,4,5,6 first-roll options, and then each of those has 6 branches for the 1,2,3,4,5,6 options on the second roll). With three different colored highlighters, give one color to the EO branches, another color to the OE branches, and the last color to the EE branches. You will see that the EO and OE branches really are different, and together are twice as numerous as the EE branches.