2024 AMC 12A Problem 16

A set of 12 tokens ---- 3 red, 2 white, 1 blue, and 6 black ---- is to be distributed at random to 3 game players, 4 tokens per player. The probability that some player gets all the red tokens, another gets all the white tokens, and the remaining player gets the blue token can be written as \frac{m}{n}, where m and n are relatively prime positive integers. What is m+n?

\textbf{(A) }387 \qquad \textbf{(B) }388 \qquad \textbf{(C) }389 \qquad \textbf{(D) }390 \qquad \textbf{(E) }391 \qquad

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.