الفهرس 
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Abstract
The aim of this thesis is to study the Whitney numbers, develop a new generalized families of these numbers and introduce a connection of them with other numbers. In addition some applications of these numbers in probability are given. The thesis is organized as follows: Chapter 1: In this chapter present, the principle combinatorial tools and some concepts of probability which we need through our study such as factorials, recurrence relations, generating functions and moments. Chapter 2: A review on some interesting combinatorial numbers such as: Whitney, Stirling, Lah, harmonic numbers and their applications in probability. Further more a survey on records and some applications for these numbers in probability are given.Chapter 3: This chapter is devoted to the generalized r-Whitney numbers of the _rst and second kind and the generalized Whitney numbers of the _rst and second kind. We obtain the recurrence relations, generating functions, and explicit formulas and give some special cases. New combinatorial identity, some relations between these numbers and other numbers and matrix representations of some relations are also given. Finally their applications in probability are derived. Chapter 4: This chapter aims to derive the multiparameter r-Whitney numbers of the _rst and second kind. We deduce the recurrence relations, generating functions, and explicit formulas and show some special cases. New combinatorial identity, some relations between these numbers and other numbers and matrix representations of some relations are also given. Finally some of their applications in probability are obtained