Sum of dice adding to less than $5$

Question

I have seen some places saying that the sum of $2$ dice being thrown being less than $5$ can occur for the cases

$$(1,1),(2,2),(2,1),(3,1),$$

giving a probability of $\frac4{36}$ for the event.

However, I have also seen people counting the numbers twice, as there are two different ways to throw the dice, giving the cases

$$(1,1),(1,1),(2,2),(2,2),(2,1),(1,2),(3,1),(1,3),$$

and a probability of $\frac8{36}$.

Which way is correct?

Answer 1

Neither is correct. The second approach is the correct one – you list all the ordered possibilities. Nevertheless, you have listed $(1,1)$ and $(2,2)$ twice.