College Algebra & Trigonometry, 2018a

Chapter 7
Combinatorics
7.1 The Fundamental Principle of Counting
Combinatorics is a major area of what is generally known as “Discrete Mathematics.”
The word discrete refers to quantities that are individual, separate or
distinct. This creates a major division in mathematics between “continuous mathematics”
and “discrete mathematics.” The difference between these two areas is
that continuous mathematics considers and uses all parts of the number line -
whole numbers, rational numbers (fractions), irrational numbers and so forth.
Discrete mathematics typically uses only the whole numbers.
Rather than limiting the possibilities in mathematics, this restriction actually opens
amazing new areas of consideration. The binary codes that computers use are
generally controlled and kept (mostly) error free through the use of discrete mathematics.
Computer security for the simplest (checking your on-line bank balance)
and the most complex (high level classified data) digital information is handled
through encryption that relies on the concepts of discrete mathematics.
Any type of application in the sciences that involves choices and possibilities often
uses the concepts of combinatorics. Combinatorial chemistry explores the
results when a series of different chemical groups are added to the same basic
chemical structure to investigate the qualities of the resulting compound. In addition,
combinatorics is very important to the study of probability. In order to
calculate the probability of an event, it is often necessary to calculate how many
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