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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
m1 ,m2 ,··· ,mk Remark:
We called Notes Basic Counting
m1 ,m2 ,··· ,mk the multinomial coefﬁcient where m
m1 , m2 , · · · , mk = m!
m1 ! × · · · mk ! 4.9 Example 13 Basic Counting
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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