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 whos on Berlusconis left, 6 ways to choose whos on that persons left, and so on. (iii) If they stand in a line, whats 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, whats the probability that Obama is next to Harper?...
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210hw11solns - Math 210 Homework 11 Solutions 1. This...

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