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Unformatted text preview: MATH 222 [A01] Fall 2011 Second Midterm Test Instructor: Dr. Jing Huang November 17, 2011 3:30 - 4:20pm Instructions: This question paper has five pages plus cover. For each question, write out your solution/answer carefully in the space provided. Use the back of pages if necessary. Marks will be deducted for incomplete or poorly presented solutions/answers. The Sharp EL-510R calculator is the only calculator permitted. No other aids (such as books, notes, formula lists, or scratch paper) are allowed. Questions Value Marks 1 5 2 3 3 6 4 4 5 5 Total 23 Name: Answer Key Id: V20111117 .../1 1 1. In how many ways can the nine letters M,A,T,H,I,S,F,U,N be permuted so that none of the words MATH , IS and FUN occurs as consecutive letters? Let U be the set of all permutations of the nine letters. Then |U| = 9!. Let S 1 ,S 2 ,S 3 ⊂ U be the sets of permutations containing MATH , IS , FUN respec- tively, We need to compute |U - ( S 1 ∪ S 2 ∪ S 3 ) | . By the Principle of Inclusion and Exclusion,...
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This note was uploaded on 01/15/2012 for the course MATH 222 taught by Professor Huangjing during the Spring '11 term at University of Victoria.
- Spring '11