You rolls a fair die $N > 6$ times and you want to rolls the sequence $1,2,3,4,5,6$ in this order.
What is the probability that the last 6 rolls were (in consecutive order) $1,2,3,4,5,6$, (So, on the Nth roll you get a 6, on the $(N-1)$th roll you get a 5, etc.), AND you did not roll this sequence any times before the last 6 rolls.
If I state another way, what is the probability that you roll the sequence 1,2,3,4,5,6 starting from the $(N-5)$th roll and you did not roll this sequence starting from any roll before the $(N-5)$th roll?
This is not a homework problems, just something I'm thinking about.