Rolling 3 dice

I'm stuck,

I need help.

Here's the problem:
When 3 dice are rolled, find the probability of getting a sum of 7.

I tried identifying the possible combination of numbers that will form a sum of 7. These are (3,3,1),(2,2,3),(4,1,2),(5,1,1).

I don't know if what I'm doing is correct and I don't what to do next.

thanks.

There is a way to do this with gernerating functions.

\(\displaystyle \left(\sum_{k=1}^{6}x^{k}\right)^{3}=x^{3}+3x^{4}+6x^{5}+10x^{6}+15x^{7}+.......+x^{18}\)

Look at the coefficient that corresponds with x^7. It is 15. That means there are 15 different ways of getting a sum of 7 when rolling 3 dice.

The total number of possible rolls is 6^3=216

Therefore, the probability os 15/216=5/72