When six unbiased dice are rolled simultaneously, the probability of getting all distinct numbers (i.e., 1, 2, 3, 4, 5, and 6) is
Answer
(B)
Explanation
Each die shows one of 6 faces independently, so there are \(6^{6} = 46656\) equally likely outcomes.
For all six numbers to be distinct, the dice must show 1 to 6 in some order. The first die can take any of 6 values, the second any of the remaining 5, and so on, giving \(6! = 720\) favourable outcomes.
\[P = \frac{6!}{6^{6}} = \frac{720}{46656} = \frac{5}{324}\]
(Dividing 720 and 46656 by their common factor 144 gives 5 and 324.)
Answer: B