# Thread: Three dice are rolled.

1. ## Three dice are rolled.

Any help appreciated, thanks.
Three dice are thrown. What is the probability that the total number of dots shown is twelve? What is the probability that the total number of dots shown is twelve and at least one or more of them shows a six?

2. How many different ways are there of making 12 when throwing 3 dice?

3. Do I just count them? because it did take a while and I think it is 25 ways of making 12.

Thanks

4. Originally Posted by shra28
Do I just count them? because it did take a while and I think it is 25 ways of making 12.
You are correct about the 25.
However, each of the twenty-five may have different probabilities.

For example $444$ can appear in only one way.
But, $255$ can appear in three different ways.
And $246$ can appear in six different ways.

$6^3=216$ Thus the $\mathcal{P}(4+4+4)=\frac{1}{216}$.