# What is the probability of rolling a 10 with three dices.

There are 6^3 = 216 possible permutations of throwing 3 dice. Of those possibilities, 27 add up to ten. They are:

1,3,6; 1,4,5; 1,5,4; 1,6,3; 2,2,6; 2,3,5; etc. up to ...6,2,2; 6,3,1

The probability of throwing 10 is therefore 27/216 = 1/8

## To calculate the probability of rolling a 10 with three dice, we need to determine the number of favorable outcomes (i.e., the number of ways we can get a sum of 10) and divide it by the total number of possible outcomes.

First, let's calculate the total number of possible outcomes when rolling three dice. Since each die has 6 sides, there are 6 possible outcomes for each die. Therefore, the total number of possible outcomes when rolling three dice is 6 multiplied by 6 multiplied by 6, which equals 216.

Next, we want to find the number of favorable outcomes, which are the combinations of rolls that add up to 10. To find these combinations, we can list out all the possible ways the dice can land to sum up to 10.

Here are the combinations that add up to 10:

1, 3, 6

1, 4, 5

1, 5, 4

1, 6, 3

2, 2, 6

2, 3, 5

2, 4, 4

2, 5, 3

2, 6, 2

3, 1, 6

3, 2, 5

3, 3, 4

3, 4, 3

3, 5, 2

3, 6, 1

4, 1, 5

4, 2, 4

4, 3, 3

4, 4, 2

4, 5, 1

5, 1, 4

5, 2, 3

5, 3, 2

5, 4, 1

6, 1, 3

6, 2, 2

6, 3, 1

Counting these combinations, we find that there are 27 favorable outcomes.

Now, to calculate the probability, we divide the number of favorable outcomes (27) by the total number of possible outcomes (216):

Probability = Number of favorable outcomes / Total number of possible outcomes

= 27 / 216

= 1 / 8

Therefore, the probability of rolling a 10 with three dice is 1/8.