# Roll 12 different dice. How many will have at least each 1,2,3,4,5,6 occurring?

• nowimpsbball
In summary, the question is asking how many outcomes out of a total of 12*6 possibilities will have at least one die showing each number 1, 2, 3, 4, 5, and 6. This is a probability question with a chance of 1/6 for each number on a single die.
nowimpsbball

## Homework Statement

12 different dice are rolled. How many outcomes will have at least one of each number 1,2,3,4,5,6 occurring?

## The Attempt at a Solution

I don't even know where to go because I really don't know what the question is asking. Does it mean how many rolls (where each roll is rolling 12 dice) must be made to get at least one of each number?

Thanks

You roll 12 dice.

Each (standard) die has 6 sides. You roll one die, it has 6 different outcomes. You then roll the second die, it has 6 outcomes. For the first two die, you could have 1-1, 1-2, 2-1, 2-2, 3-1, 3-2, 3-3, 2-3, 1-3, etc.

So, after rolling all 12 dice, you have 12*6 possibilities in total.

In how many of those possibilites will you have at least one die being a 1, one being a 2, one being a 3, 4, 5, 6..?

It seems to me like a probability question...

Since there are six numbers possible on a dice, and you have have 12 dices, the chances for any of those numbers(1,2,3,4,5, or 6) to come on a single dice is 1/6(<-- fraction). Can you figure out the rest?

pretty close goldenwing, 2 minutes difference(between my answer and yours) :)

## 1. How does rolling 12 different dice affect the likelihood of getting all numbers from 1 to 6?

The more dice that are rolled, the higher the chances of getting all numbers from 1 to 6. However, it is not guaranteed that all numbers will appear.

## 2. Is there a way to calculate the exact probability of getting all numbers from 1 to 6 when rolling 12 different dice?

Yes, the probability can be calculated using the formula (6/6)^12, which equals to approximately 2.2%.

## 3. Does the order of the numbers matter in this scenario?

No, the order of the numbers does not matter. As long as all numbers from 1 to 6 appear at least once, the outcome is considered successful.

## 4. How does the probability change if we increase or decrease the number of dice being rolled?

As mentioned before, the more dice that are rolled, the higher the chances of getting all numbers from 1 to 6. On the other hand, decreasing the number of dice will decrease the probability.

## 5. Can we use this scenario to illustrate the concept of probability in a real-life example?

Yes, this scenario can be used to explain the concept of probability in a real-life situation. For example, when rolling 12 different dice, the probability of getting all numbers from 1 to 6 is similar to the probability of winning the lottery. It is possible, but not very likely.

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