Rolling a total on an unfair die after 5 throws So I have an unfair $4$ sided die. The face values are $0,1,2,3$. 
The probabilities of throwing these face values are \begin{align}0&: 0.7\\
1&: 0.2\\
2&: 0.07\\
3&: 0.03\end{align}
I have to throw the die $5$ times.
The probability of me throwing a total of $0$ is $0.7^5$
The probability of me throwing a total of $15$ is $0.03^5$
The probability of me throwing a total of $2$ is $(0.2^2\times0.7^3)+(0.07\times0.7^4)$
This will start becoming tedious and error prone if I have to go through all $16$ outcomes especially as there are numerous paths for reaching the majority of numbers like in the example of throwing a $2$ above. 
I could do with having a table in excel that can calculate these chances for me without me doing a manual probability tree.
Is there any algorithm that I can use to calculate the probability of throwing a total of $n$ using the probability table?
Thanks
 A: Actually, you're not correct on the probability for throwing $2$. There are $_5C_2 = 10$ ways to throw three zeroes and two ones, and five ways to throw four zeroes and a two:
$$P_2 = 10 \cdot 0.2^2 \cdot 0.7^3 + 5 \cdot 0.07 \cdot 0.7^4.$$
The two other cases you did are correct, because there's only one way to throw five zeroes, as there is only one way to throw five threes.
When you get to $6$ or $7$, things get really fun.
In other words, it's even more tedious than you envisioned, unfortunately.
The $10$ and $5$ coefficients are the multinomial parts:
$$10 = \frac{5!}{2!3!} \text{ and } 5 = \frac{5!}{1!4!}$$
A: Doing it in Excel is not hard. Leave some blank lines at the top and count up in column A for the sum. Count up from $0$ horizontally starting in column B. The entries will be the probability that you get the sum on the left rolling the number of dice above. Put a $1$ in $0,0$ as if you roll no dice the sum is certain to be zero. Then fill with $0.7$ times right plus $0.2$ times right up plus the other two. The blank rows were to have zeros for negative totals and avoid the need for special formulas for sums of $0,1,2$.  Copy right/copy down is your friend.
