A six sided die is rolled 3 times what is the probability that all three rolls resulted in different numbers

For the first roll, the chances of getting any number is 6/6 or 1, since no numbers have been rolled yet.

For the next roll, the chances of getting a different number is 5/6, since 1 number has already been rolled and we don't want to receive the same number.

For the final roll, the chances of getting a different roll from the first 2 is 4/6 or 2/3, since we have already got 2 different numbers that we don't want to repeat.

Now, multiply all these fractions together.

1 * 5/6 * 2/3

= (5*2) / (6*3)

= 10 / 18

= 5 / 9

Thus, you have a 5/9 chance of rolling a different number if you roll the dice three times.