Find the probability that a particular fish is caught before two of the colors of fish are exhausted. In a particular pond there are L white, M red, and N yellow fish. One of the yellow fish is George. A fisherman catches one fish per day and stops only if two of the colors of fish are exhausted. Find the probability that George survives.
I came up with P(George survives) = ((L+M+N-1)/(L+M+N))(N/(L+M+N)).
I first tried to solve the problem by finding P(George survives not including 2 colors exhausting) = (L+M+N-1)/(L+M+N). I found this by using permutations.
Then I found probability that two colors exhausted. I figured that I only have to worry about white and red fish being exhausted, since the only way George will survive is both white and red fish are exhausted. So P(white and red fish are exhausted) = N/(L+M+N). I believe that this is correct but I am not sure.

Ignore the yellow fish other than George. Of the $(L+M+1)$ relevant fish, George must be the only one not caught. The probability of this should be quite clear:
$$\frac{1}{L+M+1}$$
