The student is familiar with the Z formulae for the expression of certain multiple-life contingencies in terms of symmetrical combinations of the component joint-life statuses. The present note develops an analogous method based upon last survivor statuses. In certain circumstances this latter type of expression may be the more convenient for practical use.

Consider a set of m lives. Then in the notation followed by E. F. Spurgeon, in his book, Life Contingencies, Zr represents the sum of the probabilities of r lives surviving a given period for all combinations of r lives that can be made out of the set of m lives. The number of combinations of r lives that can be formed out of the set of m lives is .