lecture28 - Lecture 28 Counting Announcements Hw7 posted....

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Lecture 28 Counting
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Announcements Hw7 posted. Due Apr 23. Start early! Final: Wed, May 12, 8am Smith Hall
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Basic Counting Principles The product rule Sum rule Inclusion-Exclusion |A| + |B| - |A B|
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Pigeonhole principle If k +1 or more objects (pigeons) are placed into k boxes, then there is at least one box containing two or more of the objects
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Generalized pigeonhole principle If N objects are placed into k boxes, then there is at least one box containing N / k objects
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Permutations Permutation of a set S = ordered arrangement of the elements of S Example S={1,2,3} Permutations of S are 1 2 3 1 3 2 2 1 3 2 3 1 3 1 2 3 2 1
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r - Permutation r-permutation of S = an ordered arrangement of r elements of S Example S={1,2,3} 2 Permutations of S are 1 2 1 3 2 1 2 3 3 1 3 2
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P(n,r) : number of r-permutations of a set with n elements P(n, r) = n (n-1)(n-2)…(n-r+1) = n! / (n-r)! Note: 0! = 1
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lecture28 - Lecture 28 Counting Announcements Hw7 posted....

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