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Unformatted text preview: CSE 21: Homework Solutions 3 October 12, 2009 Let S ( n,k ) be the Stirling number of the second kind which counts the number of ways to partition n labeled elements into k disjoint, nonempty, unlabeled blocks. Problem 1 In how many ways can 6 people be assigned to 4 nonempty teams? Solution: S (6 , 4). Problem 2 An urn contains 5 red marbles and 6 white marbles. (a) How many ways can 4 marbles be drawn? (b) What if we must have 2 red marbles and 2 white marbles? (c) What if all 4 must have the same color? 1 Solution: (a) ( 11 4 ) . (b) ( 5 2 )( 6 2 ) . (c) ( 5 4 ) + ( 6 4 ) . Problem 3 12 students are eligible to attend the National Students Association meeting. (a) How many ways can 4 students be selected to attend? (b) Suppose that two of the students will refuse to go if they are both se lected? (c) Suppose two of the students are married and will only go if they are both selected? Solution: (a) ( 12 4 ) . (b) ( 12 2 4 ) + ( 12 1 3 )( 2 1 ) . (c) ( 12 2 4 ) + ( 12 2 2 ) . Problem 4 5 symbol passwords must be formed using the 26 letters { a, b, ..., z } and the 10 digits { 0, 1, ..., 9 } . How many possible passwords can be formed if each one must have at least one letter and at least one digit, and cannot have both the letter o and the digit 0?...
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 Fall '07
 Graham

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