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52 Slides--Combinatorics II

52 Slides--Combinatorics II - CS103A HO#52 Combinatorics II...

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CS103A HO #52 Combinatorics II 3/5/08 1 What is |A B C| ? AB C Counted by: |A| + |B| + |C| - |A B| - |A C| - |B C| + |A B C| 8 + 6 + 7 - 3 - 3 - 3 + 2 14 Once Once Once Once Once Once Once |S D C| = |S| + |D| + |C| - |S D| - |S C| - |D C| + |S D C| A survey of 200 TV viewers found that 110 watch sports, 120 watch comedy, 85 watch drama, 50 watch drama and sports, 70 watch comedy and sports, 55 watch comedy and drama, and 30 watch all three. How many people watch sports, comedy, or drama? How many do not watch any of these categories? |S D C| = |S| + |D| + |C| - |S D| - |S C| - |D C| + |S D C| 110 + 85 + 120 - 50 - 70 - 55 + 30 170 people watch sports, comedy, or drama 30 people do not watch any of these categories A survey of 200 TV viewers found that 110 watch sports, 120 watch comedy, 85 watch drama, 50 watch drama and sports, 70 watch comedy and sports, 55 watch comedy and drama, and 30 watch all three. How many people watch sports, comedy, or drama? How many do not watch any of these categories? A survey of 200 TV viewers found that 110 watch sports, 120 watch comedy, 85 watch drama, 50 watch drama and sports, 70 watch comedy and sports, 55 watch comedy and drama, and 30 watch all three. S C D 30 A survey of 200 TV viewers found that 110 watch sports, 120 watch comedy, 85 watch drama, 50 watch drama and sports, 70 watch comedy and sports, 55 watch comedy and drama, and 30 watch all three. S C D 30 20 25 40 A survey of 200 TV viewers found that 110 watch sports, 120 watch comedy, 85 watch drama, 50 watch drama and sports, 70 watch comedy and sports, 55 watch comedy and drama, and 30 watch all three. S C D 30 20 25 40 10 20 25 30
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CS103A HO #52 Combinatorics II 3/5/08 2 |S D C| = |S| + |D| + |C| - |S D| - |S C| - |D C| + |S D C| |A B C D| = |A| + |B| + |C| + |D| -|A B| - |A C| - |A D| - |B C| - |B D| - |C D| +|A B C| + |A B D| + |A C D| + |B C D| -|A B C D| A B C D A permutation of a set of objects is an ordering of the objects. For example, the set of elements {a b c} can be ordered in the following ways: abc acb cba bac bca cab By the product rule, there are n · (n-1) · (n-2) · . .. · 2 · 1 = n!
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52 Slides--Combinatorics II - CS103A HO#52 Combinatorics II...

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