# Three dice and getting a sum of 9

What is the probability of tossing three dice and getting a sum of 9?

To calculate the probability of getting a sum of 9 when tossing three dice, we need to consider the number of ways to achieve this outcome and divide it by the total possible outcomes when rolling three dice.

There are 6 sides on each die, so there are 6^3 = 216 possible outcomes when rolling three dice.

Now, let’s find the number of ways to get a sum of 9:

1. 2-3-4: There are 3! (3 factorial) or 6 ways to arrange these numbers.
2. 1-4-4: There are 3 ways to arrange these numbers since there are two 4’s (3 slots to place the unique number 1).
3. 3-3-3: There is only 1 way to arrange these numbers, as they are all the same.

Now, add the number of ways together: 6 + 3 + 1 = 10

Divide the number of ways to get a sum of 9 by the total number of possible outcomes:

Probability = (Number of ways to get a sum of 9) / (Total possible outcomes) = 10 / 216 ? 0.0463

So, the probability of getting a sum of 9 when tossing three dice is approximately 0.0463 or 4.63%.