Numbers - PigeonHole

SOURCE:COMPETITION
Number of Problems: 2. : (Book)

 

 

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Six distinct positive integers are randomly chosen between 1 and 2006, inclusive. What is the probability that some pair of these integers has a difference that is a multiple of 5?

mathrm{(A) } frac{1}{2}qquadmathrm{(B) } frac{3}{5}qquadmathrm{(C) } frac{2}{3}qquadmathrm{(D) } frac{4}{5...

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