ABSTRACT
In a separate section, the problem of counting the number of integer
solutions of a linear equation with unit coeÆcients is reduced to a prob-
lem of enumerating combinations. Some basic elements of enumeration of
lattice paths, related to the enumeration of certain combinations, are pre-
sented. The re ection principle, which facilitates the enumeration of lattice
paths, is demonstrated. Moreover, the famous ballot problem that led to
the development of lattice paths is treated. The last section of this chap-
ter is devoted to discussion of several applications in discrete probability
and statistics. Specically, the classical probabilistic problems of the most
benecial bet and the distribution of shares, with which a systematic study
of enumeration of permutations and combinations began, are discussed. In
addition, the Maxwell-Boltzman, Bose-Einstein and Fermi-Dirac stochastic
models in statistical mechanics are brie y examined.
