A set of $10$ tokens --- $2$ red, $2$ white, $2$ blue, and $4$ black --- is to be distributed at random to $2$ game players, $5$ tokens per player. The probability that each player gets exactly one red token, one player gets all the white tokens, and the other player gets all the blue tokens can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?