Change question title if you can come up with better one
In box we have $k$ white, $m$ blue and $n$ red balls. From the box one after another we fetch all balls and we write down color of that ball. What's the probability that in our list of colors, white color will appear before a blue.
So, as I understood we can have any amount of red balls in a row and then white must appear.
For example: W, RW, RRW, RRRW, R..........W
So I need to calculate something like that: $\frac{k}{k+m+n}+\frac{n}{k+m+n}\frac{k}{k+m+n-1}+\frac{n}{k+m+n}\frac{n-1}{k+m+n-1}\frac{k}{k+m+n-2}+...$
until all red balls appeared and finally white
But I don't know what appears here and how to write it. Or maybe there's even more easier way to solve it?