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An unbiased dice, with faces numbered 1,...

An unbiased dice, with faces numbered 1, 2, 3, 4, 5, 6, is thrown n times and the list of n numbers shown up is noted. Then find the probability that among the numbers 1, 2, 3, 4, 5, 6 only three numbers appear in this list and each number appears at least once.

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To solve the problem, we need to find the probability that when an unbiased die is thrown \( n \) times, only three distinct numbers appear in the results, and each of those three numbers appears at least once. ### Step-by-Step Solution: 1. **Understanding the Problem**: We need to ensure that out of the six faces of the die (1, 2, 3, 4, 5, 6), only three distinct numbers show up after throwing the die \( n \) times, and each of these three numbers must appear at least once. 2. **Choosing 3 Numbers**: ...
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