# Sol3 - CSE 21: Homework Solutions 3 October 12, 2009 Let S...

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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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## Sol3 - CSE 21: Homework Solutions 3 October 12, 2009 Let S...

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