How to understand combination? $2$ fair tetrahedral dice each showing the numbers from $1$ to $4$ on each of their faces are rolled and their face values are added together. How can I calculate the discrete probability distribution?
My workings:


I am struggling to understand the use of combinations. So lets say I want to know the probability of sum of $3$ how can I do that? So I can get $1$ on the first die and $2$ on the second die. and I can get $2$ on the second die first and they can be counted as one? Likewise I can get $1$ on the second die and $2$ on the first die. I can also get $1$ on the second die first or second, either way they counted as one?
Can someone please provide an intuitive way to understand combination? What is I want to calculate the probability of getting a sum of 5?
So the sample space for all possible outcomes of rolling those two dice will be $S ={\{2,3,4,5,6,7,8\}}$. There are 16 different outcomes of the rolls. Only 1 of them will be equal to $2$ (when you get $1$ and $1$ on both dice), hence probability of getting a sum of $2$ will be $1/16$. To get the sum equal to $3$ you can get either $2,1$ or $1,2$ which means only two different options, so probability of sum $3$ will be $2/16$ and so on. The intuition is to calculate the possible ways of getting the sum and divide that by total possible outcomes.
So the sample space for all possible outcomes of rolling those two dice will be $S ={\{2,3,4,5,6,7,8\}}$. There are 16 different outcomes of the rolls. Only 1 of them will be equal to $2$ (when you get $1$ and $1$ on both dice), hence probability of getting a sum of $2$ will be $1/16$. To get the sum equal to $3$ you can get either $2,1$ or $1,2$ which means only two different options, so probability of sum $3$ will be $2/16$ and so on. The intuition is to calculate the possible ways of getting the sum and divide that by total possible outcomes.