The probability of a single dice Vs many dice

Say I have a fair six sided die. I throw 6 times. What's the probability the result will be 1,2,3,4,5,6 in that order?

And imagine I have 6 die and threw them at the same time. What's the probability that I'll get those numbers 1,2,3,4,5,6 when I arrange them?

I'm struggling to understand the difference here.

Answer

Case 1: The chance you throw a $1$ on the first die is $1/6$; the chance you throw a $2$ on the second die is also $1/6$; and likewise for all 6 of them. Thus the probability you get all these independent events is $P = \left( \frac{1}{6} \right)^6$.

Case 2: You roll the first die and it comes up with some number. The probability that the next ("neighbor") or "second" die is some different number is $5/6$. The probability that the third die is a number different from the prior two is $4/6$.

Can you continue?