6 dice are tossed one by one, the probability that all dice show 1,2,3,4,5,6 in that order.

Question

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6 dice are tossed, what's the probability that all dice 1,2,3,4,5,6 in that order.

Answer 1

The probability of rolling $123456$ with six dice in a single roll can be expressed as: $$P(\text {second die does not match first die})\times P(\text {third die does not match first or second die}) \times \cdots$$ $$ = 1\times \frac {5}{6} \times \frac {4}{6} \times \frac {3}{6} \times \frac {2}{6} \times \frac {1}{6} = 0.015432$$

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