  In this paper we prove asymptotic normality of the total length of external
branches in Kingman's coalescent. The proof uses an embedded Markov chain,
which can be descriped as follows: Take an urn with n black balls. Empty it in
n steps according to the rule: In each step remove a randomly chosen pair of
balls and replace it by one red ball. Finally remove the last remaining ball.
Then the numbers U_k, 0 \leq k \leq n, of red balls after k steps exhibits an
unexpected property: (U_0,...,U_n) and (U_n,..., U_0) are equal in
distribution.
