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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View Full DocumentCS103A
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 · (n1) · (n2) · .
.. · 2 · 1 = n!
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 Winter '07
 Plummer,R
 Computer Science, watch comedy

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