AMS 311: Lecture 3
Spring 2010
Generalized Basic Principle of Counting
:
If r that are to be performed are such that the first one may result in
n
1
possible outcomes,
and if for each of these
n
1
possible outcomes there are
n
2
possible outcomes of the second
experiment, and if for each of the possible outcomes of the first two experiments there are
n
3
possible outcomes of the third experiment, and if …, then there is a total of
n
1
×
n
2
×
…×
n
r
possible outcomes of the
r
experiments.
The number of distinguishable permutations of
n
objects of
k
types, where
1
n
are alike,
2
n
are alike,
,
k
n
are alike, and
k
n
n
n
n
+
+
+
=
2
1
is
!
!
!
!
2
1
k
n
n
n
n
1.4.
Combinations
Definition. An unordered arrangement of
r
objects from a set
A
containing
n
objects (
r
#
n
)
is called an
r
element combination of
A
, or a combination of the elements of
A
taken
r
at
a time.
There are
n
C
r
combinations of
r
elements chosen from
n
objects, where
!
)!
(
!
r
r
n
n
C
r
n

=
Example. Consider a set of
n
antennas of which
m
are defective and
nm
are functional
and assume that all of the defectives and all of the functionals are considered
indistinguishable. How many linear orderings are there in which no two defectives are
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 Spring '08
 Tucker,A
 Set Theory, Probability theory

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