  This paper addresses a theory of R(p,q)-deformed combinatorics in discrete
probability. It mainly focuses on R(p,q)-deformed factorials, binomial
coefficients, Vandermonde's formula, Cauchy's formula, binomial and negative
binomial formulae, factorial and binomial moments, and Stirling numbers.
Moreover, the R(p,q)-Stirling numbers of the second kind and the R(p,q)-Bell
numbers for graphs are also derived. Related relevant properties are
investigated and discussed. Finally, as a concrete illustration, the developed
formalism is displayed for the well known generalized q-Quesne deformed quantum
algebra to construct the corresponding deformed combinatorics, as a particular
case.
