We give polynomial time algorithms for random sampling from a set of c
ontingency tables, which is the set of m x n matrices with given row a
nd column sums, provided the row and column sums are sufficiently larg
e with respect to m, n. We use this to approximately count the number
of such matrices. These problems are of interest in Statistics and Com
binatorics. (C) 1997 John Wiley & Sons, Inc.