What is the likelihood of having an even distribution of answers (i.e. 2 A's, 2 B's, 2 C's, and 2 D's) across eight multiple choice questions with four possible answers each?
My friend and I tried doing this in Python 3 because neither of us have taken Statistics yet and we got different answers. I have a feeling my answer is slightly off: $\frac{2520}{65536}$ or $3.84521484375$%.
What I want to know is how I would do this mathematically?