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Rule;
Permutations;
Combinations Ordered partition
Deﬁnition An ordered partition of m objects into k distinct groups of
sizes m1 , m2 , · · · , mk is any division of the m objects into
a combination of m1 objects constituting the ﬁrst group,
m2 objects comprising the second group, etc. The
number of such partitions that can be made is denoted by
m
m1 ,m2 ,··· ,mk Remark:
We called Notes Basic Counting
Rules
Permutations
Combinations m
m1 ,m2 ,··· ,mk the multinomial coefﬁcient where m
m1 , m2 , · · · , mk = m!
m1 ! × · · · mk ! 4.9 Example 13 Basic Counting
Rule;
Permutations;
Combinations 3 people get into an elevator and choose to get off at one
of the 10 remaining ﬂoors. Find the following probabilities:
1 P(they all get off on different ﬂoors) 2 P(they all get off on the 5th ﬂoor) Basic Counting
Rules 3 P(they all get off on the same ﬂoor) Permutations 4 P(exactly one of them gets off on the 5th ﬂoor) Combinations 5 P(at least one of them gets off on the 5th ﬂoo...
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 Spring '08
 MARTIN
 Combinatorics, Counting, Probability, Basic Counting

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