# 222a2 - committee[2 2 In how many ways can ten boys and...

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MATH 222 FALL 2011, Assignment Two (due Thursday, Oct. 6 in class before the lecture begins) Show yourwork clearly. Illegible or disorganized solutions will receive no credit. 1. A 30-member mathematics department must select one person to chair the discrete mathematics committee and two other people to co-chair the calculus committee. (a) In how many ways can this be done? [1] (b) In how many ways can this be done if Professor Blue refuses to chair the discrete mathematics committee? [2] (c) In how many ways can this be done if Professor Green refuses to co-chair the calculus committee? [2] (d) In how many ways can this be done if Professor Blue refuses to chair the dis- crete mathematics committee and Professor Green refuses to co-chair the calculus
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Unformatted text preview: committee? [2] 2. In how many ways can ten boys and four girls sit in a row if (a) the boys are to sit together and the girls are to sit together? [2] (b) the girls are to sit together? [2] (c) if no two girls can sit next to each other? [2] 3. In how many ways can a gambler draw seven cards from a standard deck of 52 cards and get (a) a Fush (seven cards of the same suit)? [2] (b) four of a kind? [2] (c) at least three aces? [2] 4. Establish the following identity using a combinatorial argument 2 n 2 ! = 2 n 2 ! + n 2 . [3] 5. Show that if 122 numbers are selected from { 1 , 2 , . . . , 222 } , then one divides another evenly. [3]...
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