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Chapter 1
– Combinatorial Analysis
Permutations are arrangements of objects that are indistinguishable.
The number of
permutations of n objects is n!.
The number of permutations of n objects take r at a time is
(
29
!
!
r
n
n
P
r
n

=
The number of permutations of n objects, of which n
1
are alike, n
2
are alike, …,n
r
are
alike is
!
!
!
!
2
1
r
n
n
n
n
The number of combinations of n objects taken r at a time is
(
29
!
!
!
r
r
n
n
r
n
C
r
n

=
=
*
;
1
0
=
=
n
n
n
*
=

r
n
r
n
n
; *(4.1)
n
r
r
n
r
n
r
n
≤
≤

+


=
1
;
1
1
1
The Binomial Theorem: (4.2):
(
29
∑
=

=
+
n
k
k
n
k
n
y
x
k
n
y
x
0
The number of possible divisions of n distinct objects into r distinct groups of respective
sizes n
1
, n
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 Spring '11
 Berg
 Permutations, Probability

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