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Unformatted text preview: MATH 2602 (J1 & J2) November 7, 2006 Exam 2 14:05  14:55 Name: This is a closed book exam. No calculators allowed. Show all work. There are 75 points total. DO NOT BEGIN TEST UNTIL INSTRUCTED TO DO SO. Write out and sign the Georgia Tech Honor Challenge below. I commit to uphold the ideals of honor and integrity by refusing to betray the trust bestowed upon me as a member of the Georgia Tech community. 1 Problem 1. (a) [10 points] How many ways are there to take six distinguishable balls and put three into one distinguishable urn and three in another if the order of balls within each urn makes a difference? Explain. Since order within an urn makes a difference, number the positions in the first urn as 1,2,3 and the positions in the second urn as 4,5,6. Then there are 6 choices for the ball to go into position 1, 5 choices for the ball to go into position 2, and so on. Hence the number of ways to place these balls in the urns is: 6 · 5 · 4 · 3 · 2 · 1 = 6! (b) [10 points] How many ways are there to take six distinguishable balls and put three into one distinguishable urn and three in another if the order of balls within each urn does not make a difference? Explain....
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 Fall '09
 COSTELLO
 Math, Graph Theory, Planar graph

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