  We derive new combinatorial identities which may be viewed as multivariate
analogs of summation formulas for hypergeometric series. As in the previous
paper [Re], we start with probability distributions on the space of the
infinite Young tableaux. Then we calculate the probability that the entry of a
random tableau at a given box equals n=1,2,.... Summing these probabilities
over n and equating the result to 1 we get a nontrivial identity. Our choice
for the initial distributions is motivated by the recent work on harmonic
analysis on the infinite symmetric group and related topics.
