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# stat400lec4 - Statistics 400 Lecture 4 Methods of...

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Statistics 400 Lecture 4 Methods of Enumeration Multiplication Principle: Suppose that an experiment E1 has n1 outcomes and an experiment E2 has n2 possible outcomes. The composite experiment E1E2 has n1*n2 outcomes. Example: There are 5 seats in a classroom and 5 students registered for a class. How many seating arrangements do we have? Definition 2.2-1 Each of the n! arrangements of n different objects is called a permutation of the n objects. Example: There are only 3 seats in a classroom and 5 students registered for a class. How many seating arrangements do we have? Definition 2.2-2 Each of the n P r arrangements is called a permutation of the n objects taken r at a time . )! ( ! r n n P r n - = Ping Ma Lecture 4 Fall 2005 - 1 -

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Example : The number of ways of selecting a president, a vice president in a club which has 10 members. Definition 2.2-3 If r objects are selected from a set of n objects, and the order of selection is noted, the selected set of r objects is called an ordered sample of size r .
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