If six fair dice are rolled, what is the probability that each of the six numbers will appear exactly once?*1 point0.02090.01540.05000.0408
Question
Solution
To solve this problem, we need to understand that there are two parts to it.
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The total number of outcomes when six dice are rolled.
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The number of outcomes where each of the six numbers appears exactly once.
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Total number of outcomes: Since each die has 6 faces and we are rolling 6 dice, the total number of outcomes is 6^6 = 46656.
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Number of outcomes where each of the six numbers appears exactly once: This is a permutation problem. We have 6 numbers and we want to arrange them in 6 places. The number of ways we can do this is 6P6 = 6! = 720.
The probability is then calculated by dividing the number of desired outcomes by the total number of outcomes.
So, the probability = 720 / 46656 = 0.0154.
Therefore, the answer is 0.0154.
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