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, 2011

Combinatorics Difficulty 2.0 Junior Prove it Canada

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? (An arithmetic sequence is a sequence in which each term after the first is obtained from the previous term by adding a constant. For example, $3,5,7,9$ is an arithmetic sequence with four terms.)

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