Find the probability of rolling a total of 8 using 3 die.
I want to do this without having to write down every option individually.
Thanks for the help.
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
(6)(5)/3=10:
Proceed in that manner a few more times and we get
The probability of rolling a sum of 8 with 3 dice is