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CS 173:
Discrete Mathematical Structures
Cinda Heeren
[email protected]
Siebe
l Center, rm 2213
Office Hours: W 9:3011:30a
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View Full Document Cs173  Spring 2004
CS 173
Announcements
Homework 8 available.
Due 03/26, 8a.
Exam 2, Apr 4, 79p, Loom
is 141. Email Cinda with conflicts.
Today’s lecture covers material from Rosen, sections 4.44.5.
Cs173  Spring 2004
CS 173
Binomial Coefficients
(a + b)
2
= a
2
+ 2ab + b
2
(a + b)
3
= a
3
+ 3ab
2
+ 3a
2
b + b
3
(a + b)
4
= a
4
+ 4ab
3
+ 6a
2
b
2
+ 4a
3
b + b
4
Why am I showing this to
you?
1.
Beautiful patterns
2.
Recursive defn
3.
New type of proof
4.
Applications in more
complex counting
techniques
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View Full Document Cs173  Spring 2004
CS 173
Binomial Coefficients
(a + b)
2
= a
2
+ 2ab + b
2
(a + b)
3
= a
3
+ 3a
2
b + 3ab
2
+ b
3
(a + b)
4
= a
4
+ 4a
3
b + 6a
2
b
2
+ 4ab
3
+ b
4
What is coefficient of a
9
b
3
in (a + b)
12
?
A.
36
B.
220
C.
15
D.
6
E.
No clue
Cs173  Spring 2004
CS 173
Binomial Coefficients
(a + b)
4
= (a + b)(a + b)(a + b)(a + b)
=
a
4
4
0
+
a
3
b
4
1
+
a
2
b
2
4
2
+
ab
3
4
3
+
b
4
4
4
Binom
ial Theorem:
Let x and y be variables, and let n be any
nonnegative integer.
Then
(
x
+
y
)
n
=
n
j
j
=
0
n
x
n

j
y
j
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View Full Document
Binom
ial Theorem:
Let x and y be variables, and let n be any
nonnegative integer.
Then
(
x
+
y
)
n
=
n
j
j
=
0
n
x
n

j
y
j
CS 173
Binomial Coefficients
What is the coefficient of a
8
b
9
in the expansion of (3a +2b)
17
?
What is n?
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