The formula

gives the conditional probability of an (r1 × r2 × … × rk) k-variate contingency table (where is the entry in the cell identified by the k indices im), given all the marginal totals

and the hypothesis that the k random variables tabulated are mutually independent. This formula appears in (1) and more restricted forms can be found elsewhere in the literature. Certain criticisms have been made of the logic and clarity of the available proofs of (1); it is hoped that the alternative derivation given here will dispel any residual doubts, and will provide better insight into the nature of the problem.