210hw11solns

# 210hw11solns - Math 210 Homework 11 Solutions 1 This...

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Unformatted text preview: Math 210 Homework 11 Solutions 1. This question involves the 8 leaders of the G8 countries: Berlusconi, Cameron, Harper, Kan, Medvedev, Merkel, Obama, Sarkozy. (i) In how many ways can the 8 of them stand in a line? Answer: 8! = 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1. (ii) In how many ways can the 8 of them sit at a round table? Answer: 7! = 7 · 6 · 5 · 4 · 3 · 2 · 1. If there is no “head” of the table, we can start anywhere, e.g. Berlusconi. There are 7 ways to choose who’s on Berlusconi’s left, 6 ways to choose who’s on that person’s left, and so on. (iii) If they stand in a line, what’s the probability that Obama is next to Harper? Answer: 2 · 7! 8! = 2 8 = 1 4 . There are 2 · 7! permutations where Obama is next to Harper. (We could have either OH or HO, and we arrange 7 objects where one of the objects is a two-person “chunk”.) (iv) If they sit at a round table, what’s the probability that Obama is next to Harper?...
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210hw11solns - Math 210 Homework 11 Solutions 1 This...

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