Transcription of Discrete Mathematics - NYU Courant
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Discrete MathematicsLecture Notes, Yale University, Spring 1999L. Lov asz and K. VesztergombiParts of these lecture notes are based onL. Lov asz J. Pelik an K. Vesztergombi: Kombinatorika(Tank onyvkiad o, Budapest, 1972);Chapter 14 is based on a section inL. Lov asz Plummer: Matching theory(Elsevier, Amsterdam, 1979)12 Contents1 Introduction52 Let us count! A party .. Sets and the like .. The number of subsets .. Sequences .. Permutations .. 173 The sum of odd numbers .. Subset counting revisited .. Counting regions .. 244 Counting The number of ordered subsets .. The number of subsets of a given size .. The Binomial Theorem .. Distributing presents .. Anagrams .. Distributing money .. 335 Pascal s Identities in the Pascal Triangle.
So they decide to play cards instead. Alice, Bob, Carl and Diane play bridge. Looking at his cards, Carl says: “I think I had the same hand last time.” “This is very unlikely” says Diane. How unlikely is it? In other words, how many different hands can you have in bridge? (The deck has 52 cards, each player gets 13.)
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