Sample space for die throwing experiment I am throwing $8$ non-identical dice, and I want to find the probability of getting a sum of the numbers on the dice equal to $30$.

The number of ways of getting the sum equal to $30$ is $125588$ (using multinomial theorem).

Is this the number of favorable cases?

What will be the sample space? 

I am a little confused, please help me out...
Answer:

Number of favorable cases $ = (-1)^0 {8\choose0}{29\choose7}+(-1)^1 {8\choose1}{23\choose7}+(-1)^2 {8\choose2}{17\choose7}+(-1)^3 {8\choose3}{11\choose7} = 1560780 - 8*245157 + 28*19448-56*330 =125588$

In general, the formula for finding the distribution of sum s in throwing n dice with x sides goes like this

$$\sum_{k = 0}^{[(s-n)/x]} -1^k {n\choose k}{(s-1-xk)\choose (x-1)}$$
Answer:

Number of favorable cases $ = (-1)^0 {8\choose0}{29\choose7}+(-1)^1 {8\choose1}{23\choose7}+(-1)^2 {8\choose2}{17\choose7}+(-1)^3 {8\choose3}{11\choose7} = 1560780 - 8*245157 + 28*19448-56*330 =125588$

In general, the formula for finding the distribution of sum s in throwing n dice with x sides goes like this

$$\sum_{k = 0}^{[(s-n)/x]} -1^k {n\choose k}{(s-1-xk)\choose (x-1)}$$