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Lecture4

# 8 notes basic counting rule permutations combinations

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Unformatted text preview: ting 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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