I have four dice. Each die has 3 sides. I want to know the total amount of unique combinations*.
Die1,Die2,Die3,Die4
1,1,1,1
2,1,1,1
3,1,1,1
1,2,1,1
1,3,1,1
2,2,1,1
2,3,1,1
3,2,1,1
Etc....
- I don’t know if combinations is the right word, because I know this has a specific math meaning.
The only way I know how to solve this problem, is to draw a picture, but that takes too long. I want a formula that I can use to calculate the total amount of unique combinations. I don’t think the binomial formula will work, because I have 4 separate dice.
You have $4$ dice, each of which have $3$ sides. So there is three possible outcomes for each die. Hence total $3^4=81$ different outcomes possible for $4$ dice. The word $permutation$ is more accurate here than $combination$, since here the order of outcome is relevant, i.e., $1232$ is different from $1322$. Whereas in combination the ordering is not relevant.