The probability of a finite or dangling chain on an ideal polymer network has been derived by a simple recursive scheme. In contrast to the method of Dobson and Gordon, probability generating function formalism is not required. Equations are derived which give the finite chain probability as a function of reactant type and extent of polymerization. They cover most of the important types of network forming polymerizations. From the finite chain probability, useful property relations such as sol fraction, crosslink density, and the number of elastically effective network chains are developed.