Question-77

probability
counting

When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers (i.e., 1, 2, 3, 4, 5, and 6) is

When six dice are rolled simultaneously, we start by assuming that all possible combinations are equally likely. Now, for all six rolls to be distinct, the numbers \(\displaystyle 1\) to \(\displaystyle 6\) must occur exactly once. This can happen in \(\displaystyle 6!\) ways. The total number of outcomes in the sample space is \(\displaystyle 6^{6}\). Therefore, the required probability is \(\displaystyle \frac{6!}{6^{6}} =\frac{5}{324}\).