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Hw3 - Problem 5 10 cookies are to be distributed to 5...

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CSE 21: Homework 3 October 12, 2009 Problem 1 In how many ways can 6 people be assigned to 4 nonempty teams? 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? 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? 1
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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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Unformatted text preview: Problem 5 10 cookies are to be distributed to 5 school children so that no child gets more then 5 cookies. In how many ways is this possible? Problem 6 10 points A,B,C,D,E,F,G,H,I,J are placed in the plane so that no three are in a straight line. (a) How many triangles are formed by the points? (b) How many of these triangles have A as one of its vertices? Problem 7 How many poker hand (of 5 cards from an ordinary deck) have exactly 3 Aces? How many have at least 3 Aces? Problem 8 How many ways can 9 students be divided evenly into 3 teams? What if the teams have sizes 2 , 3 and 4? 2 Problem 9 Let Q n = 2 n X k =0 ± 2 n-k k ² (-1) k . What is the exact value of Q 1000000 ? (Hint: use the identity ( n k ) = ( n-1 k ) + ( n-1 k-1 ) and proof by induction.) 3...
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