# How many ways can the sum of three dice add up to a 10?

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The total outcomes of rolling 3 dice is 216. There are only 18 combinations that will give a sum of 10.

## How many different sums are possible with 3 dice?

There are 216 possible outcomes when three dice are thrown. Since the dice are ‘fair’ each of them has an equal probability. There are 27 different combinations that produce a sum of 10 (1–3–6, 2–2–6, etc).

## What is the expected value of the sum of three dice?

What is the expected value of the sum of three dice? – Quora. The expected value of one die is 3.5, which is the average of the dots on the six faces. Rolling three dice would give you an expected outcome of 10.5.

## How many different sums are possible with 10 dice?

These multiset permutations can also be considered as the number of possible different anagrams of a 7-letters word, in which only two different characters (⊕ and |) are used. Later we’ll use this concept to find the number of ways in which (say) 10 dice can yield a sum of (say) 31.

## How many ways can you roll a 13 with 3 dice?

Three dice are rolled. What is the probability of getting a sum of 13? – Quora. There are a total of 216 combinations in throwing of 3 dice. Therefore there are a total of 3 + 6 + 6 + 3 + 3 = 21 such combinations.

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## What is the probability of 3 dice?

Two (6-sided) dice roll probability table

Roll a… Probability
3 3/36 (8.333%)
4 6/36 (16.667%)
5 10/36 (27.778%)
6 15/36 (41.667%)

## What is the expected value of the sum of the two dice?

For example, if a fair 6-sided die is rolled, the expected value of the number rolled is 3.5. The expectation of the sum of two (independent) dice is the sum of expectations of each die, which is 3.5 + 3.5 = 7. Similarly, for N dice throws, the expectation of the sum should be N * 3.5.

## How do you find the expected sum?

The expected value of the sum of several random variables is equal to the sum of their expectations, e.g., E[X+Y] = E[X]+ E[Y] . On the other hand, the expected value of the product of two random variables is not necessarily the product of the expected values.

## How many ways can you roll a 9 with 2 dice?

How many ways can we get a 9 with two dice? 936 , which can be simplified to 14 . Therefore, the probability of rolling a 9 with two dice is 14 . 