Introduction to Probability Nader H. Bshouty Summary: Introduction to Probability Nader H. Bshouty Department of Computer Science Technion 32000 Israel e-mail: bshouty@cs.technion.ac.il 1 Combinatorics 1.1 Simple Rules In Combinatorics The rule of sum says that the number of ways to choose an element from one of two disjoints sets is the sum of the cardinalities of the sets. That is, if A and B are two finite sets with no members in common, then |A B| = |A| + |B|. The rule of product says that the number of ways to choose an ordered pair is the number of ways to choose the first element from A and the second element from B. That is, if A and B are two finite sets, then |A × B| = |A| · |B|. 1.2 Simple Counting Strings A string over a set S is a sequence of elements of S. For example, there are 8 binary strings of length 3: 000,001,010,011,100,101,110,111. A k-string over a set S can be viewed as an element of the Cartesian product Sk of k-tuples; thus, there are |S|k strings of length k. Permutations Collections: Computer Technologies and Information Sciences