SCHWEITZER 1956 Problem 10

In an urn there are balls of $N$ different colours, $n$ balls of each colour. Balls are drawn and not replaced until one of the colours turns up twice; denote by $V_{N,n}$ the number of the balls drawn and by $M_{N,n}$ the expectation of the random variable $v_{N,n}$ . Find the limit distribution of the random variable $\frac{V_{N,n}}{M_{N,n}}$ if $N \to \infty$ and $n$ is a fixed number. (P. 8)