Pairing gloves within one
You have pairs of gloves labelled with the numbers through (so ten gloves: two of each label). The ten gloves are shuffled and randomly matched into new pairs. What is the probability that every new pair consists of two gloves whose labels differ by at most ? The probability is for an integer ; find .
Show hints (2)+
- Total matchings of gloves into pairs is .
- Valid pairs join equal or adjacent labels. Count consistent matchings along the label chain –––– (it comes to ).
Answer
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45
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Asked at: Jane Street, Two Sigma