Stable husbands

Slippose n boys and n girls rank each other at random. We show that any particular girl has at least (3 E) in n and at most (1 + c) In n different husbands in the set of all Gale/Shapley stable matchings defined by these rankings, with probability approaching 1 as n + co, if e is any positive constant. The proof emphasizes general methods that appear to be useful for the analysis of many other combinatorial algorithms.