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Unformatted text preview: 4 3 + 1 2 + 2 1 + 3 . Warning : It was proved in a homework exercise that the average number of parts is (2 n + 1) / 2, but you cannot do the problem just by knowing the average number of parts. For example, the compositions in the set { 2 + 2 , 3 + 1 , 1 + 3 , 1 + 1 + 1 + 1 } have an average of (2 n + 1) / 2 parts but 3 / 4 of the compositions in the set have at most 2 parts. 4. We want to count 4bead necklaces that can be made using a supply of k > 4 dierent types of beads. (We allow rotations of a necklace, but not ipping over.) (a) How many necklaces can be made if each type of bead can be used as often as you wish? (b) How many necklaces can be made if each type of bead can be used at most once in each necklace? END OF EXAM...
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 Fall '08
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 Math

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