Dice roll probability given $n$ standard $6$ sided dice what is the probability $x$ $(x<n)$ will show $5$s and $n - x$ will all show $2$s?

Question

Dice roll probability given $n$ standard $6$ sided dice what is the probability $x$ $(x<n)$ dice will show $5$s and $n - x$ dice will all show $2$s?

I understand there is a straightforward way to solve this with binomial coefficients but I've been hunting around and cannot find any good examples against which to pattern match. Any pointers in the right direction much appreciated!

Answer 1

Think about how many ways you can choose $x$ dice to be $5$s and the probability of any individual configuration of the $n$ dice occurring.