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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? ' |
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For two numbers to have a difference that is a multiple of 5, the numbers must be congruent (their remainders after division by 5 must be the same). are the possible values of numbers in . Since there are only 5 possible values in and we are picking numbers, by the Pigeonhole Principle, two of the numbers must be congruent . Therefore the probability that some pair of the 6 integers has a difference that is a multiple of 5 is . |