# Question: When three dice are rolled How many ways can a sum of 6 be obtained?

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## How many ways can you roll a pair of dice to get a sum of 6?

Since each die has 6 values, there are 6∗6=36 6 ∗ 6 = 36 total combinations we could get.

What are the most likely outcomes from rolling a pair of dice?

Outcome Probability
6 5/36 = 13.89%
7 6/36 = 16.67%
8 5/36 = 13.89%
9 4/36 = 11.11%

## How many ways can you roll a 6 with 3 dice?

A. There is a total of 6^3=216 combinations if you roll 3 dice. There are 5^2×3=75 combinations that you will get one 6. Thus there is a 75/216=25/72 chance of getting only one 6 when rolling 3 dice.

## What is the probability of getting at least one 6 when six dice are rolled?

The expected number of dice showing 6 is 1 when throwing six dice. The probability to see at least one 6 is 1−(5/6)6, as explained in Timothy’s answer.

## What is the probability of rolling 2 dice and getting a sum of 7?

For each of the possible outcomes add the numbers on the two dice and count how many times this sum is 7. If you do so you will find that the sum is 7 for 6 of the possible outcomes. Thus the sum is a 7 in 6 of the 36 outcomes and hence the probability of rolling a 7 is 6/36 = 1/6.

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## What is the probability of rolling a sum of 8?

Probabilities for the two dice

Total Number of combinations Probability
7 6 16.67%
8 5 13.89%
9 4 11.11%
10 3 8.33%

= 91/216.