AMC 10 Step by Step
2005 AMC 10BProblem 21P21-25~4 minPrint

Forty slips are placed into a hat, each bearing a number 11 , 22 , 33 , 44 , 55 , 66 , 77 , 88 , 99 , or 1010 , with each number entered on four slips. Four slips are drawn from the hat at random and without replacement. Let pp be the probability that all four slips bear the same number. Let qq be the probability that two of the slips bear a number aa and the other two bear a number bab \neq a . What is the value of q/pq/p ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.