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.
