What is the chance that the other ball I have drawn out is also red?

Also try Daniel Liu's Expected Distance on a Circle.

Five couples like to go to the movies together; they always sit in a row of ten adjacent seats. To shake things up a bit, they have a rule that nobody is allowed to sit next to their partner. How many seating arrangements are there for this party?

I thought of this problem while watching a bad (Hollywood) movie on a bad date ;)

How many non-degenerate triangles can be formed with these dots?

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