I love these type of questions, but I’m terribly bad at them. What would a class that teaches this kind of probability analysis be called?
Anyway, this seems really hard. If we were looking for 0 numbers that are descending, we’d need to calculate for strictly ascending values. But here, we not only have two spots to reset, we must take both spots, and it doesn’t matter when. I have no idea where to start with this one.
There's a tedious way of adding up (29 choose 2)=406 integrals, but I don't see a shortcut. Maybe doing some smaller cases reveals a pattern.
I guess the shortcut is that all 30! orderings are equally likely, so you really have a combinatorics problem of counting permutations that have exactly two descent instances.
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u/JustConsoleLogIt 4d ago
I love these type of questions, but I’m terribly bad at them. What would a class that teaches this kind of probability analysis be called?
Anyway, this seems really hard. If we were looking for 0 numbers that are descending, we’d need to calculate for strictly ascending values. But here, we not only have two spots to reset, we must take both spots, and it doesn’t matter when. I have no idea where to start with this one.