Combinatorial theory is the name now given to the subject formerly called "combinatorial analysis" or "combinatorics," though these terms are still used by many people. Like many branches of Mathematics, its boundaries are not clearly defined, but the central problem may be considered that of arranging objects according to specified rules and finding out in how many ways this may be done. If the specified rules are very simple, then the chief emphasis is on the enumeration of the number of ways in which the arrangement may be made. If the rules are subtle or complicated, the chief problem is whether or not such arrangements exist, and to find methods for constructing the arrangements. An intermediate area is the relationship between related choices, and a typical theorem will assert that the maximum for one kind of choice is equal to the minimum for another kind.
The text is divided into three major segments. The first four chapters deal with problems of enumeration. Chapters 5 through 9 deal with the intermediate area of theorems on choice. Chapters 10 through 16 are concerned with the existence and construction of designs.