TITLE: Probability of All Distinct Faces When Six Dice Are Rolled
QUESTION [12 upvotes]: If six fair dice are rolled what is probability that each of the six numbers will appear exactly once?

REPLY [3 votes]: The probability of getting each number is $1/6$.
$1$ dice: The number have $6$ choices to fill, therefore $6\cdot 1/6$.
$2$ dice: Now the number has already come on the first dice so the second number has only $5$ choices, $5\cdot 1/6$
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Similarly finally the equation is $6/6\cdot 5/6\cdot 4/6\cdot 3/6\cdot 2/6\cdot 1/6$.