#spent ages trying to solve this by using the law of total probability to split it into different cases for different values of i
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combinatorics questions are so conductive to making you waste hours messing around with incredibly complicated equations only for you to suddenly realize the actual way to do it is incredibly trivial
^ the culprit
#spent ages trying to solve this by using the law of total probability to split it into different cases for different values of i#and I created some cool charts and tables doing that which had some fun patterns I figured out#but doing that did not help in the slightest with bringing me any closer to the actual solution lol#and then I was like “wait a second”#and then I had it like three minutes after that
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