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Math Exploration

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I am working on my exploratiion and am absolutely stuck after solving for n=2 through geometric probability, any ideas on solving either questions?

a) If n people go to place X and wait for 30 min each, in the span of 24 hours (one day – from midnight to midnight), what’s the probability that any two shall meet?

b) If n people go to place X and wait for 30 min each, in the span of 24 hours (one day – from midnight to midnight), what’s the probability that n shall meet each other?

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Assuming you're counting in minutes, I think you'll have to eliminate 30 minutes from the 1440 minutes (24 hours) that is available for choosing for the second person who waits, and eliminate another 30 minutes for the next person and so on seeing how you cannot have them share a single minute in the same place X. I'm not about to calculate everything or derive a formula for you, but this probably means you can only have a maximum of 48 people until they start meeting each other.

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