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What is the probability of rolling six standard, six-sided dice and getting six distinct numbers? Express your answer as a common fraction.

Apr 2, 2019

$$\text{Let's treat the dice as distinct}\\ \text{# rolls consisting of 123456} = 6!\\ \text{total # of possible rolls } = 6^6\\ P[\text{roll of 6 distinct digits}] = \dfrac{6!}{6^6} = \dfrac{5}{324}$$