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Unformatted text preview: Chapter 3.2 Counting Multiplication rule Tree diagrams Theorem 3.1: If sets A 1 , A 2 ,.A k contain, respectively, n 1 , n 2 , n k elements, there are , n 1 n 2 n k-1 n k ways of choosing first an element of A 1 and then an element of A 2 .. and finally an element of A k Example : If a test consists of 12 true-false questions, in how many different ways can a student mark the test paper with one answer to each question? Permutations n r P n n r =-! ( ) ! is the number of permutations of r objects selected from a set of n distinct objects. Example: In how many different ways can one make a first, second, third, and fourth choice among 12 firms leasing construction equipment? Combinations The number of ways in which r objects can be selected from a set of n distinct objects is ( 29 r n n r n r =-! ! ( ) ! . Example: In how many ways can one choose four people for a committee from a total of 8 people? 1...
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- Fall '03