The subject of this book is often called “combinatorial analysis” or “combinatorics”. The questions discussed are of the sort “In how many ways is it possible to …?”, or variations on that theme. Permutations and combinations form a part of combinatorial analysis, a part with which the reader may be already acquainted. If so, he may be familiar with some of the material in the first three chapters.

The book is self-contained with the rudiments of algebra the only prerequisite. Summaries including all formulas are given at the ends of the chapters. Throughout the book there are many problems for the reader. In fact the entire monograph is in large measure a problem book with enough background information furnished for attacking the questions. A list of miscellaneous problems follows the final chapter. Solutions, or at least sketches of solutions, are given in the back of the book for questions of any depth, and numerical answers are given for the simpler problems.

Helpful suggestions were given by the members of the S. M. S. G. Monograph Panel, and also by Herbert S. Zuckerman. Max Bell used some of the material with his students, and forwarded their comments to me. The witty subtitle of the book was suggested by Mark Kac. For all this help I express my appreciation.