Calculate the probability that all results are unique when rolling a six-sided die six times?

The probability that all results will be unique in six rolls of a six-sided die can be calculated as follows:

There are 6 possible outcomes for each roll. The total number of sequences of 6 rolls is 6^6.

The number of sequences with unique results is the number of permutations of 6 elements taken 6 at a time, which is 6! = 720.

Therefore, the probability:

[ P = \frac{6!}{6^6} = \frac{720}{46656} \approx 0.0154 ]

That is approximately 1.54%.

This means that the chance of getting all different numbers in 6 rolls of a die is very small.