Rolling 6 dice, what is the probability of rolling six of a kind?
1/46656
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Rolling 6 dice, what is the probability of rolling six of a kind?
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What are the odds of rolling 6 of a kind on a six sided die...
To calculate the probability of rolling six of a kind when rolling six dice, we need to understand a few basic concepts.
First, let's determine the total number of possible outcomes when rolling six dice. Each die has six sides, so the total number of outcomes for one die is 6. Since we are rolling six dice, the total number of outcomes when rolling all six dice is 6 multiplied by itself six times, which is 6^6 or 46656.
Next, let's determine the number of favorable outcomes, which is the number of outcomes that meet our condition of rolling six of a kind. There are six possible options for rolling six of a kind: 1, 2, 3, 4, 5, or 6. For each option, there is only one possible combination to achieve it, such as all dice showing either a 1, 2, 3, 4, 5, or 6. Therefore, the number of favorable outcomes is 6.
Finally, let's calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes. So, the probability of rolling six of a kind when rolling six dice is 6 divided by 46656, which simplifies to 1/7776.