Introduction
Combinations
Discrete Mathematics
Andrei Bulatov
Discrete Mathematics – Combinations
242
Previous Lecture
Rule of Sum
Rule of Product
Permutations
Discrete Mathematics – Combinations
243
Permutations with Repetitions
How many different 4letter words (not necessarily meaningful) can
be built permuting the letters of the word
COOL?
If all letters were distinct then the answer would be the number of
all permutations of a 4element set. However, in words we build we
do not distinguish two O.
So, words
are equal.
For each of the
words we are interested in, there are two words in which the two O’s
are distinguished.
Therefore the answer is
1
2
2
1
CLO
O
and
CLO
O
12
2
!
4
=
Discrete Mathematics – Combinations
244
Permutations with Repetitions
(cntd)
Theorem
.
If there are
n
objects with
indistinguishable objects of a first
type,
indistinguishable objects of a second type,
… ,
and
indistinguishable objects of a type
r,
where
,
then
there are
(linear) arrangements of the given
n
objects.
Each arrangement of this type is called a permutation with repetitions
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 Spring '10
 AndreiBulatov
 Combinatorics, 2 K, Andrei Bulatov

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