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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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The correct Answer is:
`((3^(n) - 3. 2^(n) + 3) xx ""^(6) C_(3))/(6^(n))`
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