Compute probability of random arithmetic progression triple
Problem Description
Consider the set of integers from 1 to 30, inclusive.
From this set, you are to randomly select three distinct numbers without replacement. The selection process ensures that all possible 3-element subsets are equally likely, and the order in which the numbers are chosen does not affect the outcome.
Task
Determine the probability that these three selected numbers can be arranged to form an arithmetic progression. An arithmetic progression consists of three distinct terms with a common difference.
Deliverable
Express your answer as a simplified fraction or a decimal.
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Compute probability of random arithmetic progression triple
Problem Description
Consider the set of integers from 1 to 30, inclusive.
From this set, you are to randomly select three distinct numbers without replacement. The selection process ensures that all possible 3-element subsets are equally likely, and the order in which the numbers are chosen does not affect the outcome.
Task
Determine the probability that these three selected numbers can be arranged to form an arithmetic progression. An arithmetic progression consists of three distinct terms with a common difference.
Deliverable
Express your answer as a simplified fraction or a decimal.