What is the probability of rolling six standard, six-sided dice and getting six distinct numbers? Express your answer as a common fraction.
So let's start by finding the total number of possible outcomes. This is just $6^6$ since we have 6 options for each die. Now let's find the number of outcomes where all of the numbers are distinct. There are $6$ options for the first die, $5$ options for the second die, $4$ options for the third die, $3$ options for the fourth die, $2$ options for the fifth die, and $1$ option for the sixth die. So the probability of rolling six standard, six-sided dice and getting six distinct numbers is $\frac{6*5*4*3*2*1}{6^6}$ We can simplify this to $\frac{5*4*3*2*1}{6^5}$ Which is $\frac{120}{7776}$ And the probability as a decimal is about $0.015$



