Question

What is the probability that if you roll a standard die three times, you will get three different numbers?

Answer 1

Total number of possible outcomes is $6\times 6\times 6=216$
First die we can get any number, so number of ways is $6$
Second die can get any number except the one which first die got, so the number of ways is $5$
Third die can get any number except the one which first and second dies got, so the number of ways is $4$
Therefore the total number of ways such that all three dies got different numbers is $4\times 5\times 6=120$
The probability is $\frac{120}{216}=\frac{5}{9}$.