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Three different numbers are chosen at random from the set {1,2,3,4,5}. The numbers are arranged in increasing order. What is the probability that the resulting sequence is an arithmetic sequence?

  • Math -

    Since the order has to be increasing , the only possibilities are
    1 2 3
    2 3 4 , common difference of 1 for these three choices
    3 4 5
    1 3 5 , common difference of 2
    (there are not enough numbers to have a common difference of 3)

    The total number of triplets we can form are
    5x4x3 = 60

    Prob that our triplet forms an arithmetic sequence = 4/60 = 1/15

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