Let's say I have $n$ fair 6-sided dice. What is the probability that the same set of outcomes is obtained when $n$ fair dice are rolled twice?
$n=8$: Suppose $8$ dice are rolled. If the first roll is $[1, 3, 6, 2, 3, 4, 3, 1]$, there are two 1's, one 2, three 3's, one 4, and one 6.
Rolling the same dice again, what is the probability that the next roll will also have two 1's, one 2, three 3's, one 4, and one 6?
The above example uses 8 dice, but I'm curious about the probability for any positive $n$.
My question is different than Two dice throw probability since I'm looking for the probability of $n$ dice having the same result in two consecutive throws