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CS 70
Discrete Mathematics for CS
Spring 2005
Clancy/Wagner
HW 9
Due Thursday, April 7
Coverage:
This assignment involves topics from the lectures of March 15, 17, 29, and 31, and from Rosen
sections 4.4 and 5.1. The assignment is shorter than usual because of the April 5 exam.
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Homework exercises:
1. (50 pts.)
Binomial coefficients
This question will teach you about binomial coefficients. As was explained in class, suppose we want
to count how many different ways there are to choose a subset of
m
objects from a set of
n
different
objects. Assume that repetition is not allowed, and the order in which you choose the
m
objects
is ignored. The answer, of course, is
n
!
m
!
(
n

m
)
!
. This is such an important value that we define the
notation
(
n
m
)
as shorthand for
n
!
m
!
(
n

m
)
!
. This is called the binomial coefficient “
n
choose
m
”, and you
will sometimes see it written
C
(
n
,
m
)
in other texts. As a matter of convention, if
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 Fall '08
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