Rolling dices possibility

Question

I must solve given task:

Three dice are rolled. What is possibility the sum of it to be $5$?

I guess I have to use combination formula, but I do not know the basic approach. Can you please explain. My thoughts: Sum of $5$ can be only get from numbers: $1$, $2$ and $3$. - $221$ $113$. I guess those are permutations. How must I continue?

Answer 1

There are exactly three ways to order the triplet $2,2,1$ : $(2,2,1),(2,1,2),(1,2,2)$

Similarly there are three different ways to get $1,1,3$

At the end there are $6$ different ways to get $5$ as sum among the $6^3$ possibilities $$P(X_1+X_2+X_3=5)=\frac{6}{6^3}=\frac{1}{6^2}$$

Answer 2

If the outcome the experience is a triplet$\{d_1,d_2,d_3\}$ with the scores of each of the three dice, you have $6^3$ possible outcomes, all with the same probability.

$3$ of these are a permutation of $1-1-3$ and $3$ are a permutation of $1-2-2$

$6$ favourable outcomes in an universe of $6^3$ possible outcomes gives you a probability of $6^{-2}$ of reaching a sum of $5$.