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Unformatted text preview: Quiz 5 Solutions Dilip Raghavan December 6, 2008 Problem 1. Let U be the set of all possible arrangements of the 26 letters without any repetitions. Let A 1 be the set of arrangements with the word INCH. Let A 2 be the set of arrangements with the word LOST, and let A 3 be the set of arrangements with the word THIN. We want to count A 1 A 2 A 3 . First of all, U = 26!. Now for  A 1  , we treat INCH as one symbol, and so we have 23 symbols to arrange. So  A 1  = 23!. The same for  A 2  and  A 3  . For  A 1 A 2  , we treat INCH as one symbol and LOST as another symbol, and so we are arranging 20 symbols. So  A 1 A 2  = 20!. Next, for  A 2 A 3  , since there must be no repetitions, the only possibility is for LOSTHIN to be one symbol. So again we are arranging 20 symbols, and so  A 2 A 3  = 20!. For  A 3 A 1  , notice that it is impossible to have both THIN and INCH occurring because some letter will be repeated. So  A 3 A 1  =...
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 Spring '11
 Raghaven

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