Expectation · Cards · difficulty 2 of 5
Out-of-order pairs
You shuffle 10 cards numbered 1 to 10, so every order is equally likely, and lay them out in a row. An out-of-order pair is two cards, anywhere in the row, where the larger number comes before the smaller one. What is the expected number of out-of-order pairs?
Answer with an expected value. First lock in a gut guess with an 80% range, then solve it properly, then watch a simulation settle on the truth.
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