A recursive solution to an occupancy problem resulting from TDM radio communication application (Q1294258)

This mathematical note is treating the following interesting occupancy problem: which is the probability that \(m\) and \(n\) boxes each have exactly one ball, resulting from distributed \(k\) balls into \(n\) boxes? The solution to this problem is given by a set of recurrent (recursive) expressions. Numerical results are obtained by translating the obtained formulae into an adequate computer program. This occupancy problem may be applied to obtain solutions to multiple access problems of Time Division Multiplexing (TDM) radio communication systems.