ics141-lecture23-Combinatorics1

# ics141-lecture23-Combinatorics1 - 23-1ICS 141 Discrete...

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Unformatted text preview: 23-1ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiICS141: Discrete Mathematics for Computer Science IDepartment of Information and Computer SciencesUniversity of HawaiiStephen Y. Itoga23-2ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiLecture 23Chapter 5. Counting5.3 Permutations and Combinations23-3ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiSome material in these slides were taken/adapted from the slides made by Prof. Michael P. Frank and Prof. Jonathan L. Gross which are provided through the publisher of “Discrete Mathematics and Its Applications” written by Kenneth H. Rosen.Some slides were done by Prof. Baek23-4ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiPermutationsA permutationof a set Sof elements is an orderedsequence that contains each element in Sexactly once.E.g. {A, B, C} → six permutations: ABC, ACB, BAC, BCA, CAB, CBAAn orderedarrangement of rdistinct elements of Sis called an r-permutationof S.The number of r-permutations of a set with n=|S| elements is.,nrrnnrnnnnrnP≤≤-=+---=)!(!)1()2)(1(),(…23-5ICS 141: Discrete Mathematics I (Spr 2008)University of HawaiiPermutation ExamplesExample: Let S = {1, 2, 3}.The arrangement 3, 1, 2 is a permutation of S (3! = 6 ways)The arrangement 3, 2 is a 2-permutation of S (3·2=3!/1! = 6 ways)Example: A terrorist has planted an armed nuclear bomb in your city, and it is your job to disable it by cutting wires to the trigger device. There are 10 wiresto the device. If you cut exactly the right three wires, in exactly the right...
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ics141-lecture23-Combinatorics1 - 23-1ICS 141 Discrete...

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