a - A pair of dice is thrown 11 times. What is the probabiliy that the eleven possible values of their sum are obtained once each (this can be solved by simple probability theory).
b - if the pair of dice is thrown 12 times, what is the probability that the eleven possible values of their sum are obtained at least once each
In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.