The total number of combos is
Can you expand this?. Look at the coefficient of the x term whose exponent is 8. That's the number of ways it's possible to sum to 8 with 3 dice.
The expansion will start with x^3 and the first coefficient is 3. So, we have , thus far.
Now, to find the next coefficient, multiply the coefficient of the x^4 term by the exponent 4 and divide by one less than the preceding exponent. (3)(4)/2=6
Proceed in that manner a few more times and we get
The probability of rolling a sum of 8 with 3 dice is