253 days until 2017

Discrete Mathematics Level 5

Consider the set of these 1008 consecutive odd numbers\( S={3,5,7,\ldots,2017}\)

Now I randomly choose 673 distinct elements of \(S\). What is the probability (in percent) that there exists 3 co-prime numbers among the chosen ones?

Give your answer to the nearest integer.

Bonus: Generalize it!


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