This book provides a treatment of counting combinatorics and contains topical discussions beyond what is typically seen in other related books.   Formulas are discussed and justified, and examples include unique approaches and ideas to the discussed topics.  The applications do not advance beyond the use of Venn diagrams, the inclusion/exclusion formula, the multiplication principal, permutations, and combinations.   For example, the author presents poker hand problems that count the number of bracelets that can be made with n > 1 different colored beads followed by the number of derangements of {1, . . . , n}.  The book's second theme presents the case by case method for solving problems. Formulas are presented when needed, but readers are asked to think mathematically and in exactly the same way from problem to problem throughout the book.  Each chapter covers no more than one topic each, and coverage includes such topics as logic and paradoxes; sets and set notation; power sets and their cardinality; Venn diagrams; the multiplication principal; permutations; combinations; problems combining the multiplication principal; problems combining permutations and combinations; and problems involving the complement rule.  In addition, derangements, elementary probability, conditional probability, independent probability, and Bayes' Theorem are addressed. The book concludes with a discussion of two dimensional geometric simplex algorithm problems, showing that the traditional geometric method breaks down in the case where variables take on only integer values.