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Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ....., 20}. The probability that the chosen numbers when arranged in some order will form an AP is $\frac{1}{85}.$ If the four chosen numbers from an AP, then the set of all possible values of common difference is ${?1, ?2, ?3, ?4, ?5}.$
  • AIEEE - 2010
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  • Probability