Compute probability of random arithmetic progression triple

Q: Compute probability of random arithmetic progression triple

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Question

You have the integers from 1 to 30 inclusive.

You randomly choose 3 distinct numbers without replacement, and all 3-element subsets are equally likely. The order in which the numbers are drawn does not matter.

What is the probability that these three numbers can be arranged to form an arithmetic progression (three distinct terms with a common difference)? Express your answer as a simplified fraction or decimal.

Compute probability of random arithmetic progression triple

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