Compute probability of random arithmetic progression triple
Company: Mavensecurities
Role: Data Scientist
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Take-home Project
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.
Quick Answer: This question evaluates combinatorics and probability skills, specifically counting combinations and recognizing arithmetic progression structure among distinct integers, and belongs to the Coding & Algorithms category for Data Scientist roles.
Return the simplified probability that three distinct numbers chosen from 1..30 form a three-term arithmetic progression.
Constraints
- Return the reduced fraction as a string.
Examples
Input: ()
Expected Output: '21/406'
Explanation: There are 210 arithmetic-progression triples among C(30,3)=4060 subsets.
Hints
- Clarify edge cases before coding.
- Keep the return value deterministic.